Electroluminescent cooling (ELC) of light-emitting diodes (LEDs) generally requires very high light emission efficiency. Earlier studies of electroluminescence and photoluminescence suggest that temperature strongly affects the light emission efficiency and, therefore, it is useful to explore the temperature range below room temperature (RT) where ELC might be easier to observe. With that purpose in mind, we electrically characterized four differently sized (0.2, 0.5, and 1 mm diameter) test devices, consisting of LEDs coupled with integrated photodetectors, at temperatures ranging from 100 K to 300 K to investigate how the temperature affects the efficiency of the structures in practice. We found that, for the studied devices, both the quantum efficiency and the overall efficiency indeed increase for low temperatures and reach peak values at temperatures clearly below RT. We also found that the temperature at which the peak efficiency occurs shifts toward higher values as the absolute value of the efficiency increases.