In order to further improve the energy utilization of the range extender electric vehicle (REEV), the energy management strategy of the REEV under different heat demands and operating temperatures is studied. Firstly, for reducing the extra fuel consumption caused by engine operating temperature, the influence of engine lubricating oil temperature on the equivalence factor is analyzed, and a novel method is proposed, which can determine the equivalence factor by three parameters, including engine temperature, operating condition type, and battery state of charge (SOC). Secondly, to reduce the influence of frequent engine start/stop on fuel consumption, a method to establish the penalty factor based on battery SOC is proposed. Finally, the engine temperature rise law under low-temperature environment and the compressor drive mode determination method under high-temperature environment are studied according to the heat demand under different ambient temperatures. An adaptive equivalent consumption minimization strategy (ECMS) considering the effect of temperature under different heat demands is proposed on the basis of the above research. The simulation under the worldwide harmonized light vehicle test cycle (WLTC) drive cycle reveals that by using the adaptive ECMS, the vehicle operating cost is reduced by 5.69% in normal temperature environment, 0.53%-2.39% in a low-temperature environment, and 0.2%-2.01% in a high-temperature environment.