The error caused by thermal deformation is one of the main factors affecting the accuracy of CNC machine tools. Correspondingly a thermal error prediction method based on CNN-GRU combined neural network is proposed to reduce the impact of thermal error on the accuracy of CNC machine tools. By conducting thermal error experiments, the temperature rise data and thermal error data of the linear feed system of a specialized CNC machine tool are collected for spiral surfaces. Then the fuzzy c-means clustering and grey relation analysis are carried out to screen temperature sensitive points in the feed system, and a CNN-GRU thermal error prediction model is established using temperature rise data of temperature sensitive points and thermal error of feed system as data samples. To verify the accuracy and practicality of model, a comparative analysis is conducted with traditional thermal error prediction models based on CNN-LSTM and LSTM. The results showed that the CNN-GRU model possesses the high prediction accuracy and robustness, whose average absolute error, root mean square error, and determination coefficient of the prediction results are better than those of the CNN-LSTM model and LSTM model. The proposed thermal error model can lay the foundation for subsequent error compensation and provide ideas for predicting thermal errors in CNC machine tools.