In high-speed and high-precision feed systems, the thermal errors are mainly caused by the non-uniform temperature variations and time-varying thermal deformations under different operating conditions. The research work undertaken herein ultimately aims to develop a generic method which is capable of evaluating the temperature rises of heat sources (such as supporting bearings and ball screw nut) and thermal positioning error of the feed system induced by varying operating conditions (feed speed, cutting load, and preload of ball screw). Experiments were carried out on a high-speed feed system experimental bench, and the influences of operating conditions on temperature rises of supporting bearings and ball screw nut were analyzed. Based on wavelet neural network and NARMA-L2 model, the relationship between temperature rise of supporting bearings and operating conditions was established. Furthermore, with the temperature of ball screw nut set to be a moving heating source load, the temperature and thermal deformation distributions of ball screw under bearings and ball screw nut heat sources were simulated. The experiment and simulation results show that the recommended modeling method can be used to predict thermal positioning errors of feed system with good accuracy. The work described lays a solid foundation of thermal error prediction and compensation in a feed system under varying operating conditions.