The European Space agency is highly interested in a full atmospheric reentry from low Earth orbit conditions using an automatic lifting body. In this respect, a numerical method is performed to estimate the heat transfer conditions at the rear surface of a stainless steel material through solving the heat equation. The proposed models should be easily invertible in order to reconstruct the heat flux. The present study presents the analytical modeling of a 2D thermal diffusion which will be compared to different approximations: Taylor approximation, Padé approximation and finite difference method. A benchmark is developed and the temperature output measurements are compared with the proposed approximations.