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