A transient heat conduction problem, in which a frictional heat source is uniformly distributed over a square region on the surface of a half-space and varies in time, has been considered. Two states are studied, linear and oscillatory velocity, and a threedimensional numerical model, using the ADI method, is developed to calculate temperature and thermal resistance while start-up and stopping. The effects of aspect ratio, steady-state velocity, start-up and stopping times, and frequency are examined.