The effect of temperature on oil-water separations is studied in this paper, focusing on the changed penetration velocities of water droplets on the separation membrane in a horizontal separator. A compact numerical scheme is developed based on the phase-field model, and the temperature effect is first theoretically analyzed regarding the key thermodynamic properties that may affect the separation performance. The computational scenario is designed based on practical horizontal separators in the oil field, and the droplet motions in the oil-water two-phase flow are simulated using our scheme under various operation conditions. It was found that a higher temperature may result in a faster penetration of the water droplets, and a larger density difference in the oil-water system is also preferred to accelerate the separation using membranes. Furthermore, increasing the operation temperature is proved to benefit the separation of water and heavy oil.