Temperature-dependent measurements of the pulsed light-current characteristics of InGaN light-emitting diodes that were thermally annealed at different temperatures have been investigated. A distinct light output, at a fixed current density, with operating temperature arises where the light output increases as the operating temperature is reduced from 300 K, reaches a maximum, and then decreases with subsequent reductions of the operating temperature. We observe that light-emitting diodes thermally annealed at higher temperatures, which is believed to increase the number of electrically activated acceptors in the p layers, have a lower light output below 300 K and the maximum light output shifts to higher operating temperatures. Measured absorption and emission spectra show that the thermal anneal process has not affected the structure of the quantum wells within these samples. The light output, for a fixed current density, has been simulated as a function of operating temperature, and we find that by changing the concentration of acceptor atoms, compensating donor atoms, and the hole mobility in the p layers, the trends observed experimentally can be reproduced. On the basis of the simulations we find that the distinct behavior of the light output with operating temperature is due to the combination of Shockley-Reed-Hall recombination, at operating temperatures around 300 K, and electron drift leakage, at operating temperature below 300 K, and the increase of the acceptor concentration results in an increased electron drift leakage due to the change of the concomitant hole mobility. The simulations support the view that the experimental observations can be explained through changes of the acceptor concentration in the p layers when the thermal anneal temperature is increased.