This report deals with a derivation of heat conduction equation for plate bending analysis and an application of the thermal buckling problem of a thin plate. In the plate, temperature distribution of the direction perpendicular to the plate surface is assumed to be linear function. A finite element formulation of a thermal buckling problem of plate is also performed. As an application of our formulation, a thermal buckling problem of the plate subjected to local heating on the plate surface is analyzed. We can obtain buckling temperature from the finite element analysis. Also, under the transient analysis of temperature, we can estimate when the buckling occurs.