  We present a theoretical and experimental study of the damping process of the
atomic velocity in Sisyphus cooling. The relaxation rates of the atomic kinetic
temperature are determined for a 3D lin$\perp$lin optical lattice. We find that
the damping rates of the atomic temperature depend linearly on the optical
pumping rate, for a given depth of the potential wells. This is at variance
with the behavior of the friction coefficient as calculated from the spatial
diffusion coefficients within a model of Brownian motion. The origin of this
different behavior is identified by distinguishing the role of the trapped and
traveling atoms.
