Figure 3 shows the effect of applying the maximum *p* correction (*λ*(max*p*), considering no *T* correction) and the maximum *T* correction (*λ*(max*T*), considering no *p* correction) on ambient *λ* values (see Table 2). For comparison, the *T* calculated with no *p*/*T* correction on *λ* is given. Obviously, the *T* differences between the different approaches increase strongly with depth. Based on the respective *p* and *T* correction applied, the possible in situ *T* values may deviate from the non-corrected *T* profile. The maximum difference between *λ*(max*p*) and *λ*(max*T*) could be used as an indicator for the uncertainty of *T* prognosis using correction functions. It accounts for about 8 °C at 2 km depth and to about 55 °C at 8 km depth, respectively. At the same time, the *T* dependency of *λ* is, compared to the *p* dependency of *λ*, more pronounced. Although the model scenarios contain different rock types exhibiting different thermophysical parameters, these general observations are the same. However, the rock parameterization gives rise to thermal anomalies in both scenarios. For section A, the radioactive (hot) magmatic monzonite (unit B, Table 2) in the depth interval 2–4 km (Fig. 1) causes a positive thermal anomaly below 3.5 km depth, while the higher *λ* value of the granitic unit above the monzonite body (unit C) is responsible for a decrease in *T* in that area (see *T* profile at 2 km depth, Fig. 3). The high *λ* value of the basaltic rock complex in the eastern part of section A (unit I) causes the comparably low *T* values in that section to a depth of about 5 km. For section B, the most prominent feature in the *T* pattern is due to the salt structures, providing great contrasts in *λ* values. Due to the chimney effect of the higher conductive salt, *T* is increased at the salt diapir by about 5 °C close to the surface (section B, 0.5 km). The same chimney effect at the salt diapir is responsible for lower *T* values (compared to surrounded profile km) at depths of 2.0–8.0 km, with a maximum deviation at about 3.5 km depth. If instead of the correction function sediments_{VS}, the correction formula salt_{ZH} is applied for the salt unit, the chimney effect would slightly increase, however, not changing the overall pattern of the *T* field. Whereas the maximum *T* and *p* corrections account for the maximum possible influence on the simulated thermal field (Fig. 3), the possible influence of a combined correction is shown in Fig. 4.

Due to the differences in thermal properties of the modeled rock units in scenario A, the resulting *T* distribution for a certain depth level shows a much larger range relative to sedimentary scenario B (Fig. 4). In the calculation, a minimum *p*/*T* correction (based on the presented single corrections for *p* and *T*) and a maximum *p*/*T* correction was considered. Based on the selected correction functions for scenario A (Table 2), different ways of combination of *p*/*T* corrections are applied on *λ*: *λ*(*p*,*T*) with the minimum case *λ*(max*p*,min*T*) and the maximum case *λ*(min*p*,max*T*), *λ*(*T*,*p*) with the minimum case *λ*(min*T*,max*p*) and the maximum case *λ*(max*T*,min*p*), and *λ*(*p* + *T*) for the minimum case. For the maximum case, *λ*(*p* + *T*) will show the same results as *λ*(*p*,*T*) because the applied *T* correction is following an additive manner. In 10 km depth, the uncertainty amounts to about 30 °C and increases towards greater depths (not shown in Fig. 4). For scenario B, the same type of combinations of *p*/*T* corrections was considered. However, in scenario B, the maximum case (maximum *T* and minimum *p*) refers to no p correction (Table 2, scenario B), therefore (although the applied *T* correction is not additive), *λ*(min*p* + max*T*) equals *λ*(min*p*,max*T*) (not shown in Fig. 4b). For both scenarios, calculating *T* based on *λ*(max*p* + min*T*) yields slightly larger *T* differences than based on *λ*(max*p*,min*T*). In comparison, the bandwidth of the *T* range for a given depth and correction mode is less pronounced for the sedimentary scenario than for the magmatic–metamorphic cross section (scenario A). This is related to the geometry and the parameterization of scenario A, which is less structurally manifold than scenario B and introduces also lateral heat flow, resulting in a greater *T* variation. Depending on the configuration of the correction approach, *T* may differ by about 40 °C in 8–10 km depth.

To shed more light on the possible effects on the *T* field as function of the geological setting and the linked thermal properties, Figs. 5 and 6 show a selection of *T* and Δ*T* profiles of certain positions along the 2-D section for the igneous and the sedimentary scenario, respectively. The uncorrected *T* profiles (upper part of Figs. 5 and 6) depend on the respective model parameterization and the basal heat flow condition. Thus, the *T* gradient changes with respect to *λ* of the involved model polygons. For the igneous scenario, the possible effect of *p*/*T* corrections is given by the *T* difference originating from the different correction modes and for an increased and a reduced basal heat flow. Corrections considering the *p* dependency of *λ* may result in a reduction of about 20 °C compared to uncorrected parameters at 10 km depth, while considering only the *T* dependency may end up with *T* estimates increased by more than 40 °C compared to *T* based on uncorrected *λ* and a basal heat flow of 30 mW m^{−2} (at 30 km depth). Bordered by the two lines of maximum *p* and *T* corrections (given by *λ*(max*p*) and *λ*(max*T*) in Fig. 5) is the branch of possible in situ *T* conditions. Applying the maximum effect of a combined correction (by correcting firstly for *p* and subsequently for *T* or vice versa) has a strong impact on the modeling result. Remarkably, the effect of a *λ*(max*T*) or a *λ*(*T*,*p*) correction on the temperature is on the same order of magnitude as an increase (or decrease) of the basal heat flow in the order of 25% while not applying a correction method of *λ* (resulting in a Δ*T* of about 28 °C at 10 km depth, see upper panel of Figs. 5 and 6). If *T* corrections of *λ* are applied, a 25% reduction in basal heat flow (22.5 mW m^{−2}) results in a less pronounced effect on *T*, while a 25% increase in heat flow (37.5 mW m^{−2}) produces a much greater uncertainty of the calculated *T*.

Figure 6 shows the situation for the sedimentary scenario. If we compare the influence of an increased or reduced basal heat flow on the calculated *T* correction of *λ* and the thermal field, the situation is similar to the igneous case: the higher *T* of an increased heat flow is responsible for an enhanced *T* correction of *λ* and, thus, a higher Δ*T* (Fig. 6, upper and lower panels). In contrast to the general-rock-type correction applied for the igneous scenario (Fig. 5, Table 1), a lithotype-specific scenario (accounting for reasonable rock-specific corrections, see Table 2) is presented in Fig. 6, in addition to applying the extreme corrections [*λ*(max*p*) and *λ*(max*T*)]. While the maximum effect of an applied p correction or *T* correction is similar to the igneous scenario, resulting in a Δ*T* of − 20 °C (*λ*(*p*)) or + 40 °C (*λ*(*T*)) at 10 km depth (with a heat flow of 30 mW m^{−2}), the graphs of a combined *p*/*T* correction of the lithotype-specific scenario show a much narrower min/max range of about 20 °C (for *λ*(*p*,*T*)) to 25 °C (for *λ*(*T*,*p*)).

A distinctive feature of the sedimentary setting in scenario B is the presence of rock salt, which shows a λ higher than most common sedimentary rocks. The rock-specific combined *p*/*T* corrections (*λ*(*p*,*T*) and *λ*(*T*,*p*) in Fig. 6) do honor the salt-specific *p*/*T* dependency formulations (Table 2). They result in a stronger reduction of the ambient *λ* and do not correct for *p* effects, thus lead to comparable higher *T* values, very close to the maximum *T* correction [*λ*(*T*)] in the salt diapir (a3, b3, c3 in Fig. 6). If, however, a non-salt specific correction formula is applied (e.g., using sediments_{VS} and rocks_{FF} for *T* and *p* correction, respectively), the *T* is very close to the *T* profile based on the uncorrected ambient *λ* values for the uppermost 7 km (λ, Fig. 6).

We additionally applied the Emirov et al. (2017) *p*/*T* correction approach to the sedimentary scenario B, assuming that all sedimentary rocks show a similar thermal characteristic as the sandstone investigated in their study (*λ*(EM), Fig. 6). The resulting *T* profile (or Δ*T* in Fig. 6) of the *λ*(EM) correction shows a remarkable *T* contour: it follows more or less the reference *T* profile (based on ambient and uncorrected *λ* values), indicating also slightly lower values for the uppermost 10 km of the crust. Moreover, it is more or less in line with the no-salt scenario [*λ*] for the uppermost 5 km indicating that it may be a valid approach for siliciclastic rock types. However, at greater depths, *λ*(EM) deviates significantly from the other correction modes.