Spin-coating is a common method of making thin polymer films. Recent experiments show that polymer films produced by this method are highly nonequilibrated. By monitoring the temporal evolution of the surface structure of freshly spin-cast polystyrene films on Si with molecular weights, 2.3 <= M-w <= 393 kg/mol, we find that the relaxations can be fully accounted for by thermal excitations of surface capillary waves on the film surface. Modeling of the data based on this relaxation scheme leads to excellent agreement between the viscosity of the films and that of the bulk polymers. Our results provide compelling evidence that thickness uniformity is the major cause of the nonequilibration of the films.