The thermal accuracy of the spindle is the main reason for the decline of precision CNC machine tools. The traditional datadriven thermal accuracy modeling method emphasizes the optimization of modeling algorithms and ignores the analysis of thermal accuracy characteristics, resulting in low robustness, poor interpretation, and complex model structure. In this regard, the thermal accuracy characteristics of the spindle are analyzed from the perspective of data mechanism, and a thermal accuracy modeling method is proposed. Temperature-sensitive points (TSPs) need to be selected before thermal accuracy modeling, and the LASSO algorithm is used to realize the adaptive TSPs selection. Based on quantile regression analysis, it is proved that the TSPs have double variability, and the compound quantile regression algorithm is used to improve modeling accuracy. The variable operating conditions tend to reduce the generalization ability of the model. The L2 regularization algorithm is used to improve the robustness of the model. Therefore, the thermal precision modeling method of spindles based on composite quantile regression and elastic network regularization is proposed. The experiments show that the thermal error of the machine tool after compensation using the proposed modeling method fluctuates within ±2 μm, an increase of 93. 3% compared to before compensation. The proposed modeling method has advantages in prediction accuracy, robustness, adaptability, and interpretation.