In this work, an extended temperature current–voltage (I–V) model for AlGaN/GaN high electron mobility transistors (HEMTs) is proposed. Since there is no carrier freeze‐out effect in GaN HEMTs, the current density, switching characteristics, and heat dissipation performance are significantly improved with the decrease in temperature. The threshold voltage drift phenomenon can be accurately described at various temperatures by the trapping effect control potential model. Based on Matthiessen's law, the applicable temperature range of the mobility model is further extended. At cryogenic temperatures, the saturation current, saturation velocity, and sub‐threshold swing of the device tend to saturate as well as be temperature‐independent, which can be accurately modeled by using the equivalent temperature and applying the crucial temperature to quantify the turning point. Furthermore, the SHE modeling incorporates the temperature dependence of the material's thermal conductivity. The accuracy of the model is verified by experimental data at low (4.2–300 K) and high (298–773 K) temperatures. The proposed model overcomes the limitations of existing models applied at wide ambient temperatures.