In transient laser-induced grating experiments, the diffusion coefficients and lifetimes of free excitons are determined in CdSe at temperatures between 2 and 40 K and for different densities. We find that the diffusion coefficient D decreases and that the recombination lifetime ${\mathit{T}}_{1}$ increases with increasing temperature. The increase of ${\mathit{T}}_{1}$ with temperature is due to the release of excitons bound to impurities and to an increase of the radiative lifetime. From the measured D values for motion parallel and perpendicular to the crystal c axis, we extract momentum relaxation rates which are discussed in terms of exciton-acoustic-phonon scattering. In pure samples, and for lattice temperatures T10 K, the interaction via the deformation potential is dominating, while for higher temperatures, the interaction via the piezoelectric potential becomes significant.