Using Bragg scattering as a sensitive probe, we study how atoms are cooled and localized after the sudden turn-on of 1D and 3D optical lattices. We measure the time evolution of the mean-square position spread of the atoms in the lattice potential wells, a quantity proportional to their effective temperature. The rate of exponential approach to equilibrium is proportional to the photon scattering rate and about 6 times faster in 1D than in 3D. This simple proportionality was unexpected, based on the usual model of Sisyphus cooling, but is in agreement with our 1D Monte Carlo simulations.