Abstract: The actuator to be applied to the Xinjiang Qi Tai Radio Telescope needs to maintain an accuracy of ±15 μm in a temperature range of -40~60 ℃. The thermal error can reach about 400 μm without any compensation. Therefore, it is necessary to establish a thermal error model to predict the change law of actuator displacement with temperature. And active displacement control compensation is carried out to ensure that the actuator can meet the requirements of positioning accuracy at a given temperature. First of all, from 16 temperature points, combining the basic requirements of the model and the significance test, a series of screenings are performed to select the temperature points suitable for the model. Then use the gray prediction theory to establish the gray prediction model for the actuator. Finally, the prediction model was optimized according to the actual situation. The research shows that: this paper innovatively adopts the method of combining statistics with engineering practice to select the temperature measurement point, and the thermal error model can guide the actuator displacement active control compensation, so that the actuator can achieve the positioning accuracy of ±4 μm in the required temperature range of -40~60 ℃.