We calculate scattering rates of QW excitons by acoustic phonons using realistic deformation potentials for electrons and holes in structures based on GaAs. We use these rates 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 QW size. The exciton distribution function reaches a stationary shape after the luminescence passes through its maximum. This shape shows strong deviations from the thermal-equilibrium distribution, at least for temperatures below 50 K. As a consequence, exciton radiative recombination is slower than the usually expected thermal average of the radiative rate. We discuss the dependence of this effect on the well width.