Resumo: This work presents a study of three methods to solve an inverse heat conduction problem: direct inversion, backward integration, and the least square method. The best performance is achieved with the least square method. The inverse problem aims at the determination of the initial condition from a temperature profile measured at time $t = \tau > 0$. The direct problem models the heat conduction in a slab with insulated boundary conditions. A spectral method is used to solve the direct problem for the least square inversion method. This inverse problem is typically ill-posed problem in the Hadamard sense. Therefore, a regularization function is used to guarantee a stable solution for the inverse problem. In this study, three regularization techniques are considered: zeroth-order and first-order Tikhonov techniques, and regularization based on maximum entropy principle.