We have studied GaInN/GaN quantum well structures grown by LP-MOVPE by picosecond time-resolved photoluminescence spectroscopy. For the quantum wells we find rather long PL decay times of up to 600 ps at low temperature. At temperatures higher than about 100 K, the decay time decreases rapidly, reaching about 75 ps at room temperature. From measurements of the integrated PL intensity, we conclude that this decrease of the decay time is due to nonradiative recombination processes. By combining our data for the lifetime and the intensity, we derive the radiative lifetime, which is constant at low temperature and increases at elevated temperatures. We explain this behavior on the basis of the interface roughness at low temperature and thermal dissociation of excitons at higher temperatures.