In a layered thermal conductor, the inaccessible interface could be damaged by mechanical solicitation, chemical infiltration, aging. In this case, the original thermal properties of the specimen are modified. The present paper deals with nondestructive evaluation of interface thermal conductance h from the knowledge of the surface temperature when the specimen is heated in some controlled way. The goal is achieved by expanding h in powers of the thickness of the upper layer. The mathematical analysis of the model produces exact formulas for the first coefficients of h which are tested on simulated and real data.