The combined effect of a short carrier lifetime and of phonon emission on the cooling rate of nearly resonantly excited carriers in bulk GaAs has been investigated using picosecond time-resolved photoluminescence. Intense photoexcitation of carriers results in very short carrier density decay times of about 20 ps, leading to a considerable reduction of the cooling rate. The rapid density decay is attributed to a high stimulated recombination rate due to a high density accompanied by a low effective carrier temperature. Inclusion of the stimulated recombination in a model calculation for the energy relaxation by phonon emission leads to a significant recombination heating, which nicely explains the observed reduction of the carrier cooling rate.