The accelerating structures of modern supercolliders, as well as the components of high-power microwave electron devices operated in strong cyclic electromagnetic fields should have long lifetimes. Along with the electric breakdown, the surfaces of these microwave components deteriorate and their lifetimes decrease due to thermal strains and subsequent mechanical loads on the surface metal layer. The elementary theory of thermal fatigue was developed in the 1970s. In particular, a model of metal as a continuous medium was considered. Within the framework of this model, thermal fatigue is caused by the strains arising between the hot surface layer and the cold internal layer of the metal. However, this theory does not describe all the currently available experimental data. In particular, the notion of “safe temperature” of the heating, i.e., temperature at which the surface is not destroyed during an arbitrarily long series of pulses, which was proposed in the theoretical model, is in poor agreement with the experiment performed in the Stanford Linear Accelerator Center (SLAC, USA). In this work, the thermal-fatigue theory is developed on the basis of consideration of the copper polycrystalline structure. The necessity to take it into account was demonstrated by the results of the SLAC experiment, in which a change in the mutual orientation of copper grains and the formation of cracks at their boundaries was recorded for the first time. The developed theory makes it possible to use the experimental data to refine the coefficients in the obtained formulas for the lifetime of the metal surface and to predict the number of microwave pulses before its destruction as a function of the radiation power, the surface-temperature increase at the pulse peak, and the pulse duration.