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The thermal error is a significant factor that influences the machining accuracy of machine tools, and error compensation is an economical and effective method for enhancing the accuracy of machine tools. However, establishing a precise thermal error prediction model is crucial for thermal error compensation. In this paper, the subtraction-average-based optimizer-based CNN-GRU neural network (SABO-CNN-GRU) is applied to integrated thermal error modeling. Through conducting a thermal characteristic experiment, temperature rise data and thermal error data were collected from the linear feed system of LXK300X helical groove CNC machine tool. The fuzzy c-means clustering and grey correlation analysis are employed to identify temperature-sensitive points in the linear feed system. By utilizing the temperature rise data from these sensitive points along with feed shaft thermal errors as data samples, and using the SABO algorithm to optimize the CNN-GRU prediction model, the thermal error prediction model of SABO-CNN-GRU is established. To validate its superiority and practicality, a comparative analysis is conducted with traditional thermal error prediction models based on CNN-GRU and SO-ELM. The results demonstrate that SABO-CNN-GRU model outperforms both models in terms of mean absolute error (MAE), root mean square error (RMSE), remaining prediction deviation (RPD), mean square error (MSE), and determination coefficient (R2) in accurately predicting results. Building upon this achievement, this paper develops a real-time thermal error compensation system which effectively reduces maximum thermal errors from 80.5 to 17.6 μm after implementing compensation measures. Effectively reducing the influence of thermal errors and improving the machining accuracy of machine tools. [ABSTRACT FROM AUTHOR]