Scattering rates of quantum-well excitons by acoustic phonons are calculated using realistic deformation potentials for electrons and holes in structures based on GaAs. These fates are used in order to reproduce the exciton dynamics in a time-resolved photoluminescence experiment. Rise time and decay time of the luminescence signal are studied as a function of temperature and quantum-well size. It is found that the exciton distribution function reaches a stationary shape during the radiative recombination and shows strong deviations from the thermal distribution. As a consequence, the decay time is slower. A discussion of the dependence of these effects on the well width is given.