In this article, we investigate the behavior of InGaN–GaN Multiple Quantum Well (MQW) photodetectors under different excitation density (616 µW/cm2 to 7.02 W/cm2) and temperature conditions (from 25 °C to 65 °C), relating the experimental results to carrier recombination/escape dynamics. We analyzed the optical-to-electrical power conversion efficiency of the devices as a function of excitation intensity and temperature, demonstrating that: (a) at low excitation densities, there is a lowering in the optical-to-electrical conversion efficiency and in the short-circuit current with increasing temperature; (b) the same quantities increase with increasing temperature when using high excitation power. Moreover, (c) we observed an increase in the signal of photocurrent measurements at sub-bandgap excitation wavelengths with increasing temperature. The observed behavior is explained by considering the interplay between Shockley–Read–Hall (SRH) recombination and carrier escape. The first mechanism is relevant at low excitation densities and increases with temperature, thus lowering the efficiency; the latter is important at high excitation densities, when the effective barrier height is reduced. We developed a model for reproducing the variation of JSC with temperature; through this model, we calculated the effective barrier height for carrier escape, and demonstrated a lowering of this barrier with increasing temperature, that can explain the increase in short-circuit current at high excitation densities. In addition, we extracted the energy position of the defects responsible for SRH recombination, which are located 0.33 eV far from midgap.