The conservation of subterranean cultural heritage sites, particularly those located in karst environments, presents significant challenges due to the complexity of coupled thermal and geological processes. This study addresses the thermal behavior of Lascaux Cave (France), a UNESCO World Heritage site, by developing a 3D heterogeneous thermal model of the surrounding rock mass. The cave is approximately 235 m long, with up to 30 m of overlying rock mass. A geological partitioning was performed using electrical resistivity tomography (ERT) data and machine learning, allowing the rock mass volume to be divided into distinct clusters with homogeneous physical property. An inverse modeling framework, based on the Nelder–Mead simplex algorithm, was employed to estimate the optimal thermal diffusivity of each cluster. An objective function incorporating both phase shift and amplitude damping of periodic thermal signals was introduced to reduce sensitivity to uncertainties in initial temperature conditions. The results demonstrate that heterogeneity in thermal properties significantly influences the spatial distribution of temperatures and improves the accuracy of model predictions compared to conventional homogeneous approaches. This modeling approach provides valuable insight into the cave's thermal regime and establishes a foundation for predicting key conservation-related processes, such as natural convection, condensation, and localized degradation. Future work will focus on integrating the influence of water content and hydrological variations on heat transfer in the rock mass.
