A p+-i-n+ self-cooled light-emitting diode with type-II band offset is numerically simulated in one-dimension to examine the underlying cooling/heating mechanisms. The Peltier effect is confirmed to be the dominant cooling mechanism under forward bias, even when the carriers are injected without an energy barrier. Meanwhile, Joule heating in the active layer is identified as the main heating mechanism for bandgaps below 0.52 eV under an ultra-low forward bias. In contrast to non-radiative recombination, electroluminescence itself is found to be a cooling mechanism, producing most photons above the bandgap of the active layer. However, this effect only becomes noticeable under an ultra-low bias in very small bandgap materials. While it is desirable to inject more carriers to leverage larger band offsets for a higher cooling power, Joule heating limits the maximum cooling power achievable. With small band offsets (<0.21 eV), a reverse bias instead of a forward bias may become the best cooling condition, where non-radiative generation processes are discovered to be the dominant cooling mechanisms.