Abstract: Thermal post-buckling analysis of functionally graded beams is of great significance for the practical implementation of functionally graded materials for the thermal insulation of spacecrafts. The governing equations of the functionally graded beam in thermal environment are obtained based on the geometrical nonlinear theory and the introduction of the physical neutral surface. By simplification, a fourth-order integral-differential equation with respect to transverse deformation is obtained, and the eigenvalue problem is solved with the clamped boundary condition. The thermal post-buckling and the vibration on the basis of the buckled configuration are investigated. Firstly, the governing equations obtained by the Hamilton's principle are proved to be approximate equations obtained by the axial extension theory. Then, considering the heat effect on the properties of the material, the influence of the slenderness ratio, functionally gradient index and temperature ratio on post-buckling vibration is analyzed in detail. The heat effect on the properties of the material can be neglected when the slenderness is large enough. Increasing the slenderness ratio, functionally gradient index or temperature ratio will increase the non-dimensional thermal buckling load.