The effects of the thermal annealing temperature and time on the strain mechanisms involved in thin copper films deposited on a silicon substrate with a polyimide sublayer in between were studied by optical, atomic force and scanning electron microscopy. Thermal compressive stresses are shown to be responsible for buckling of detached film regions and for film wrinkling accompanied by coherent viscoelastic straining of the intermediate sublayer. Copper films are wrinkled during transformation of polyimide into a highly elastic state when the annealing temperature is above the polyimide vitrification point. Variations of the wrinkling parameters under thermal loading are found to be due to relaxation of normal and tangential tensile and compressive stresses distributed periodically along a wavy film-sublayer interface.