The manuscript by Bekesi et al. entitled ‘Modelling transient thermal processes in the lithosphere: application to the NW Pannonian basin’ presents a simplified modeling study on the thermal evolution of the NW part of the extensional Pannonian basin considering distinct crustal and mantle thinning factors and sedimentation. The calculated new thermal field is then used to present a 2D yield stress section of the lithosphere. Finally, the manuscript contains a brief discussion on mantle xenoliths. Given the large number of major issues of the manuscript, I suggest substantial revision before considering it for publication.

1. The title does not reflect the content of the manuscript. Reconstructing the thermal evolution of the lithosphere and particularly the deep lithospheric mantle is challenging, indeed, because of the large number of transient effects, i.e. partial melting, melt emplacement, phase changes, shear heating, non-uniform upper crustal, lower crustal and mantle thinning, paleo-surface temperature variations, basin inversion and related deformation, water circulation, etc. This manuscript uses the stretching factors approach of Royden and Keen (1980) to somehow consider crustal and mantle thinning in a simplified way, but none of the other transient effects are taken into account.
2. The abstract and the manuscript claims that one of the main goals is to better quantify the thermal field in the entire lithosphere. There are too problems with this: (1) the model does not use any observational constraints from the deep basins, crust or lithosphere, and likely it is not sensitive to temperature variations at great depths; therefore, the goal cannot be reached with this method. (2) While the manuscript presents one possible model result, , a sensitivity analysis, assessing the role of different initial and boundary conditions and input parameters are missing, therefore, it is not an easy task to see how robust or reliable is the model. No model limitation section is included, despite the large number of assumptions the authors made.
3. The used model parameters: Many parameters are not justified and seem to be far from reality. The source of other input data is not clarified and thus cannot be checked. A model needs to be reproduceable by the community and you need to make available the most important input data. 1. Initial crustal thickness: the authors assume a constant 35 km thickness. What is the source of this parameter? The study area includes metamorphic core complexes, their formation requires a thick and hot crust, which infers that your chosen initial values are lower than it should be. Previous reconstructions (e.g. van Hinsbergen et al. 2020) reported a much larger amounts of extension and a thicker initial crust. Geochemical studies based on xenoliths inferred a much larger initial crustal thickness (Torok et al.). Finally, the basement units of the region derived from the Alps, likely having a much thicker crust than 35 km in the Early Miocene. The initial lithospheric thickness of 120km: what is the constraint on this and how much role does it have? Lithologies: what is the source of this? For instance, the sand to shale ratio is proposed to be 1:9 for the ‘Lower Pannonian‘ (Upper Miocene). How is this constrained? After a brief google search, well logs published by Stano et al. 2016 shows a sand to shale ratio of at least 50%. This means that your applied thermal conductivities are wrong, and this is a major issue.  The timing of extension: in the model a uniform timing for rifting is assumed between 18-10. Most structures are inferred to be active only until the Middle Miocene (e.g. Majcin et al. 2015), a few small-offset normal faults would not have influenced lithospheric thinning.
4. The model result: this is already a mixture of discussion and describing some results. How is it possible that nearly 0 crustal thinning is calculated for the Rechnitz core complex area, that must have undergone substantial crustal thinning? This is a sign of the wrong model parameters. In Figure 6, it is not possible to read the values of the mismatch between the well and model data, but it still seems to be a significant error. About sediment blanketing: in the results of the shallow temperature field chapter you write: “Positive anomalies are the reflection of sediment blanketing, meaning the insulating effect of sediments with low thermal conductivity.” – The deposition of cold sediment would lead to decreased temperature values at shallow depth and higher thermal values in the basement because of the blanketing of low conductivity sediments.
5. How did you consider the uplift of the basin margins linked to the ongoing inversion of the basin (e.g. Bada et al. 2007)? Likely it would have a major impact.
6. Structure of the manuscript: The results and their discussion are not separated. You should make clear which parameters and which model outputs are well constrained and what is the sensitivity of others.
7. Comparison with previous studies: this manuscript doesn’t even mention previous modelling efforts on the crustal and mantle thinning, surface heat flow and basin temperature evolution. In the detailed comments below, you find many useful papers that can be used to compare your results with previous inferences. Besides well data, vitrinite information is also widely available in the region that should be used to validate such models.
8. Because of the many limitations listed above, the final sentences on the new stress envelope or comparison with xenoliths remain elusive and in general they don’t really connect with the manuscript. Instead, you should discuss the sensitivity and reliability of the thermal model and compare it with previous inferences and with other similar regions.

further detailed comments:

Title: it does not reflect the content of the manuscript

Abstract: reliable thermal evolution is not modelled for the entire lithosphere due to the limitations of the modelling approach and lack of constraints

ln 19-20: not all the sedimentary basins are extensional

ln 22: Royden and Keen 1980

ln 32: most thermo-mechanical models are constrained by observations, e.g. Lescoutre et al. 2019;  Heckenbach et al. 2021; many others

ln 37: in the upper crust

ln 44: sometimes you include Late Miocene, in other places you write Early to Middle Miocene. Which is true?

ln 47: how is this inversion stage considered in the model?

ln 53: i.e. compositional changes through sedimentation: what does this mean?

ln 54-56: you should reflect on the large number of previous thermal modelling efforts in the region, including, but not limited to: Lankreijer et al. 1999; Majcin et al. 2015; Bartha et al. 2018; Balasz et al. 2021; Rybar and Kotulova 2023

ln 59: "high precision" - can you elaborate?

ln 59: for (not to)

ln 73: lower plate with respect to what? Out of context.

fig. 2: what is the sedimentary basin on the right side? Also indicate the orientation of the section.

ln 87: justification?

ln 91: delete -

ln 95: where is this thickness map presented, shown? 

ln 100-101: justification?

ln 118-120: rephrase

table 1: what about paleogene rocks?

table 1: what is the source of information behind this data?

ln 128: is it available or the most important data now made available with this manuscript?

ln 135: meters?

ln 136:  in fact I cannot see too many wells in the deep basins. Elaborate

Figure 3: scale of the basement depth map?

ln 161: what about different amounts of upper and lower crustal thinning, likely affecting the Rechnitz region?

ln173: sensitivity of this assumption? What if the initial lithopsheric thickness was lower or higher?

ln 174-175: In this model, when the lithosphere was thinned to ca. 60 km, you had a 60 km depth domain of constant temperature beneath? How reliable is this?  Why dont you use a constant heat flow lower boundary condition?

Ln 180: so your model is only accurate until 5-10 km depth?

Ln 190: instead of this, it would be more useful to write about the thinning factors of the study area

Ln 196: grammar

Ln 198-200: what is the limitation of this?

Table 2: Lab: 120 meters?

Ln 204: There are many other studies calculating different crustal and mantle thinning, e.g.:   Lankreijer et al. 1995; 1999; Majcin et al. 2015; Bartha et al. 2018; Balasz et al. 2021; Rybar and Kotulova 2023

Ln 205: Primary?

Ln 206: what does past-extension mean?

Ln 209: why 35 km?

Fig. 5: how would you discuss these patterns?

Ln 259-263: this is discussion, not results

Ln 275: I would respectfully challenge this statement. How can you be sure that the deposition of cold sediments would increase the temperature in such shallow depth? It would increase at larger depth. Of course, you have higher temperature values, where the crust is thinner and therefore the mantle is more elevated.

Figure 7: which wells are these, what is the source of information? Is it open-source? At least the used and presented well data should be better documented and shared with this manuscript. It is also a warning sign how the errors increase with depth which questions the reliability of the models.

Ln 294: ref

Fig. 10: on the well data the basin was much shallower, which is right? Furthermore, it is not likely that the crust would be laterally homogenous, therefore it is difficult to understand the value of this cross-section.

Dear Eszter and coauthors,

The manuscript about modeling transient thermal processes in the lithosphere in the NW part of Hungary presents a method to assess deep lithosphere temperatures. The transient conductive heat transport equation is solved, and the calculated temperatures are fitted to observed temperature data to constrain the subcrustal stretching factor. The transient model considers the two most relevant processes, which were active during the evolution of the area: lithospheric stretching and sedimentation. The modeled lithosphere temperatures are used to deduce rheological inferences and estimate the depth of origin of mantle xenoliths found in the region. It is a valuable manuscript, but I suggest modifications and clarifications before publication.

The past and present temperatures are calculated by solving the transient conductive heat transport equation (Eq. 2). The calculated temperature depends on the initial conditions, the thermal parameters and the vertical velocity v_z. You fix these quantities except the vertical velocities related to stretching, thus the results are valid for this specific model. Other choice of the quantities probably would result different stretching factors and different lithosphere temperatures. In the following I will discuss the effects of thermal conductivity of sediments and the sedimentation rate.

The thermal conductivity (TC) of sediments in the model ranges from 1.2 W/mK to 2 W/mK (Table 1). These values are lower than the ones measured on clastic sedimentary rocks from Hungary (ranging from 1.5 W/mK to 5 W/mK in Dövényi and Horváth, 1988; Dövényi et al., 1983, shales: 2.3 ± 0.56 W/mK, sandstones: 3.75 ± 0.71 W/mK summarized in Mihályka et al. 2024). Based on the measured TC values Dövényi and Horváth (1988) established TC-depth trends for shales and sandstones, which result in higher TC than used in the study. The TC of carbonates is also lower than the measured ones. For conductivity of carbonates in Hungary see Dövényi et al. (1983). (limestones: 2.7 W/mK, dolomites: 4.4 W/mK).

As the model temperatures are fitted to the observed values, we would expect lower heat flow using the model TC’s compared to the observed heat flow. You provided the model results and the thermal parameters in an asset for reviewers, and I calculated the model heat flow in the depth interval 1000-1200 m (Fig R1). The modeled heat flow is uniform in the area: 70 ± 3 mW/m². Except the Zala basin and part of the Danube basin, where the observed values are 90 mW/m² and 85 mW/m², respectively, the modeled heat flow is close the to the observed one (disregarding also the Transdanubian range, where groundwater flow occurs). Better fit to the heat flow could be achieved by varying the TC, heat production and subcrustal stretching factor, but it was not the purpose of the study as you mentioned in the manuscript.

In Eq. 2 constant sedimentation rate is applied. Over the center of the basins, where sedimentation took place in Quaternary, the constant sedimentation rate is a good approximation. In the peripheral parts of the basins erosion has been taken place since Pliocene due to basin inversion and uplift. (See e.g. the seismic sections published in Szafián et al. (1999), a paper you refer.) Erosion increases the subsurface temperature thus, in the peripheral parts less lithospheric stretching is required to obtain fit to the observed temperatures.

As it is demonstrated varying the TC of sediments and sedimentation/erosion rate would change the modeled T and heat flow. The question arises: how much is the uncertainty of the derived stretching factors and the calculated deep lithosphere temperature?

Please make an estimate of the uncertainty of the stretching factor and the lithosphere temperature.

My questions and notes related to the text are the following.

Lines 107-108The sediment bulk thermal conductivities were finally obtained using the geometric mean of the bulk matrix conductivities and the thermal conductivity of the pore fluid.

How much was the porosity?

Line 148 outflow temperatures were marked by uncertainties of ±5 ºC,

Do you mean outflow temperature as temperature at the well head?  Well head T is unreliable, the error can be much more than ±5 C.

Line 184 What kind of numerical method did you use to integrate Eq. 2?

The last term in the equation is a partial derivation.

Line 211 Eq.3 is mistyped. It is correctly: (Z_{crust init}- Z_basement )/Z_{Moho present}.

Line 259 temperatures up to 170 ºC, meaning a geothermal gradient of ~45 ºC/km

gradT=(170-12)/4=39.5 C/km

Lines 262-263 Negative anomalies can be attributed to outcropping/near-surface basement rocks (mostly carbonates) having significantly higher thermal conductivities

Near Sopron and Rechnitz the lower temperature is partly caused by lower lithospheric stretching relative to the basin areas.

Lines 264-265 The conductive assumption is although not fully valid for parts of the Transdanubian range built up by fractured and karstified carbonate rocks.

A larger area than the Transdanubian rage is affected by groundwater flow and convective heat transport, because groundwater flow also occurs in the carbonate rocks covered by sediments.

Line 270, Fig. 6. The grey color code to visualize the difference between model and observed temperatures is not suitable to quantify the difference.

Lines 322-324 Towards the Transdanubian Range (Balaton Highland), predicted model temperatures are slightly higher in the deeper part of the model compared to the NW part (Sopron Mts.). This might be explained by the shift in the timing of active rifting, that migrated from NW towards SE (e.g. Balázs et al., 2016).

The rifting time was fixed in the model, so the temperature difference has a different reason, e.g. different subcrustal stretching factors.

Line 329 we compared the overall misfit between modelled and observed temperatures

How did you calculate the difference between the modeled and observed temperatures as they belong to different depths?

Lines 349-351 It must be noted that the predicted subcrustal stretching might not be entirely correct due to changes in the timing of stretching throughout the study area but provide a realistic picture for the degree of lithosphere attenuation.

It is not only the timing of stretching, which influences the stretching factors, but all parameters used in Eq. 2.

Lines 366-368 These differences in shallow temperature predictions can partly be explained by the different calibration datasets used by Lenkey et al. (2017) and (Lenkey et al., 2021), excluding temperature measurements from (recent) geothermal wells documented in the OGRE database.

OGRe (2020) is a very useful database to get quick-look temperature data. However, no information is given about the conditions of the measurement. E.g. it is not known if the BHT value is corrected or not. In the Geothermal Database of Hungary (Dövényi, 1994, Lenkey et al., 2021) the observed data are corrected if possible, and every temperature data is quality checked, and depending on the type and conditions of the measurement they are ranked into a quality categories. 

Lines 398-399 give references to Porkoláb et al.