The large deflection equations for a thin shallow shell are modified to include thermal effects. The temperature is considered to be an arbitrary function of the space coordinates.The resulting equations are used to study thermal buckling and post-buckling behavior of a simply supported cylindrical shell panel, subjected to a parabolic temperature distribution along its axial direction. It is assumed that the temperature is constant across the thickness of the shell and along its circumferential direction. Buckling charts for various curvatures, Ky, and aspect ratios, λ, are presented for two cases of edge conditions. In one case the edges of the panel are free to displace, and in the second case the edges are restrained.The critical temperature is found to fall outside the practical temperature range of the material for Ky ≥ 200 in the free-edge condition and for Ky ≥ 50 in the restrained-edge condition.