<p>The feed axis system of computer numerical control (CNC) machine tool is affected by temperature changes and axial loads during the machining process, which reduces the position accuracy of CNC machine tools. Due to the complexity of processing conditions and the difficulty in error detection, the formation mechanism of position error in actual working conditions is still vague. The purpose of this paper is to investigate the evolution of position error under thermal–mechanical coupling loads and identify, evaluate, and predict the position error. First, the formation mechanism and influencing factors of position error are clarified through theoretical analysis. Secondly, based on cluster analysis, the distribution of temperature measurement points is optimized to select the thermal key points which best reflect the impact between temperatures and errors. Finally, experimental data are used to decompose and evaluate the evolution process of the position error curve and the motion state of the feed axis, radial basis function neural network (RBFNN) is employed to model and predict the position error under thermal–mechanical coupling loads. The findings of this paper can help trace the source of position error and accurately assess the operating status of the machine tool.</p>