The relaxation of thermal stress in a thin film adhering to a substrate of differing expansion coefficient is discussed. It is pointed out that adhesion between film and substrate constrains relaxation so as to render grain boundary diffusion ineffective in relieving the bulk of the stress. Model calculations based on a state variable approach suggest that the required bulk deformation process is plastic flow. A qualitative picture of stress relaxation is developed which indicates that, under favorable circumstances, local plastic deformation may control the kinetics of long-range mass transport. Consideration of the interaction of plasticity and grain boundary diffusion during a temperature cycle suggests a mechanism whereby hillock volume on the film surface increases during repeated cycles.