Heat transfer between corium pool and concrete directly governs the ablation velocity of concrete in the case of molten core-concrete interaction (MCCI) and, consequently, the time delay when the reactor cavity may fail. Numerical tools dealing with MCCI generally consider that the ablation velocity of concrete is higher than the "velocity" of heat transfer inside the concrete so that conduction heat transfer in the basemat is not taken into account. With such modeling, concrete ablation goes on until the heat flux between the corium pool and the concrete is zero. This assumption proved to be satisfactory for high heat flux because of the low thermal diffusivity of concrete. Nevertheless, it can be discussed in cases where the heat flux between the corium and the concrete is "low" that is in the long-term phase of MCCI or in cases with a strong imbalance in the power splitting at the corium pool boundaries. In such situations, the heat transfer by conduction in the concrete is no longer negligible and can lead to the end of the concrete ablation. Heat conduction in the concrete could be taken into account by solving multi-dimensional transient heat transfer equations in the concrete. A spatial meshing of the basemat is then necessary, but such an approach is time-consuming. That is why a simplified one-dimensional transient approach has been chosen and implemented in the TOLBIAC-ICB code. The main purpose of this paper is to present this approach. The validation has been performed by comparing the results of this method with experimental data obtained from studying the thermal response of polymethylmetacrylate and concrete to a heat flux. Results of the model are also compared to the solutions obtained by the numerical resolution of the discretized heat transfer equation on a fine mesh. Finally, an application to the reactor case is proposed.