The emission quantum yield of carbocyanine dye J-aggregates decreased 4-fold when temperature increased from 20 to 80 K. Independent measurements of the emission quantum yield and decay were used to calculate both radiative and nonradiative rate constants in the temperature range of 4-140 K. The radiative lifetime is found to linearly increase as temperature rises and is explained by the two-dimensional structure of J-aggregates assuming thermal distribution of excitons with the requirement that only excitons with a small value of the center-of-mass wave vector can recombine radiatively. Nonradiative relaxation becomes efficient with a rise of temperature and is explained by exciton self-trapping.