To produce a good machine tool, the thermally induced error in the machine during machining plays a crucial role and is an important issue needing to be resolved. The thermal error may account for 70% of the total error. There are three main approaches to solving the thermal error problem: preventing heat flows from hot components, designing a thermally stable structure for the machine, and compensating the thermal error using thermal error models. The first two approaches can be carried out in the primary design stage of machine tools, and they have been used in the manufacture of commercial products. The third approach, the strategy of thermal error compensation, is the most effective and popular approach. However, there are still many unsolved problems. Among these problems, the cutting conditions have a significant influence on the modeling precision of the thermal error. In this study, we develop an integral model based on the integrated grey system theory (IGST) in conjunction with a genetic-algorithm (GA)-optimized back-propagation neural network (BPNN) to investigate the influence of cutting conditions on a machine tool’s thermal error. The model is chosen on account of its high ability in dealing with a small amount of training data. Results show that a single thermal error modeling formula cannot make accurate predictions for different cutting conditions. Suitable adjustment of the modeling parameters or the use of a multiple modeling scheme is needed.