Temperature dependence of the photoresponse in two superlattice infrared photodetectors with different single barriers is studied. It is found that the short-wavelength response decreases with temperature, but the long-wavelength one increases. The crossing point of those two response ranges is independent of temperature. The movement of its associated wavelength under different biases is investigated and analyzed. The relevant physical mechanisms are found and integrated into a simple model to explain the experimental results. Based on the model, another sample with a superlattice integrated with multiple quantum wells is designed to demonstrate whether its temperature dependence of the photoresponse is consistent with our understanding. The sample indeed shows a broadband response which enhances with temperature in all wavelengths.