To reduce the influence of temperature field on the machining accuracy of machine tools, we analyze the heat source composition and the thermal error mechanism in the production process of CNC machine tools, select 4 key points for temperature-measuring from the original 8 temperature-measuring points according to the theory of grey relational degree, and establish a grey (4,1) prediction model. The model builds the mapping relationship between the changes of the 4 key points and the thermal error of machine tools. It can predict the thermal error of machine tools in real time by acquiring the temperature of the key points and then compensate the predicted thermal error to the tool feed position, and thus a machine thermal error compensation mechanism is formed. The precision horizontal machining center experiment THM6380 is taken as the experimental object, the gap between the test results of GM(4,1) model and the actual thermal error value is calculated, and the fitting residual error is within ±1 μm, which shows the fitting effect is good.