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The enhancement of the conservation conditions of cave paintings requires a detailed understanding of heat transfer in such cavities. This article presents a numerical investigation of turbulent free convection in a parallelepipedic cavity. Non-homogeneous wall temperatures are prescribed from a large-scale model taking into account external temperature fluctuations damped by heat diffusion in the rock massif above the cavity. Large Eddy Simulation is performed to solve the turbulent flow fields for a given wall temperature field corresponding to a Rayleigh number of 8.5 x 109. The outcomes of the model are analysed in terms of statistical mean. Results show complex large scale flow patterns with regions of high turbulent intensity. The Q-criterion is used to identify turbulent structures for an instantaneous flow field. Then we analyse the spatial distribution of the conductive heat flux at the walls to locate the regions with intense convection. We show that the conductive flux smaller than the wall-to-wall radiative flux in the major part of the cavity, and close to its value at some spots.