The brittle coatings, made of different materials, when subjected to elevated temperatures and in the heat exchange conditions, are susceptible to delamination. Those coatings, as well as thin films, can be used for various thermo insulating deposits, e.g. in turbines of thermal power plants., In layers made of different materials, due to the environmental temperature change, thermal stresses appear as a consequence of a difference in their thermal expansion coefficients. In this paper driving forces were analyzed causing delamination of one layer from the other, i.e. the interfacial fracture in the two-layered, bimaterial sample. This analysis was limited to considering the sample behavior when exposed to the stationary temperature field. The energy release rate G, which is the driving force for this interfacial fracture, is changing with temperature and that variation is increasing with increase of the temperature difference between the environment and the sample. Analysis of this relation can be used to predict the maximal temperature difference, which the two-layered sample can be subjected to, without appearance of delamination between layers.