The cooling of a photoexcited exciton distribution in wurtzite GaN is studi
ed by time-resolved photoluminescence measurements on the longitudinal opti
cal phonon replicas of the free exciton. The temperature of the excitons de
creases for low sample temperatures within 150 ps down to the lattice tempe
rature. We derive an explicit formula for the transient exciton temperature
in terms of cooling via deformation potential scattering with acoustic pho
nons. [S0163-1829(99)51112-0].