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This study establishes a Bayesian-optimized gated recurrent unit (BO-GRU) thermal error prediction architecture, aiming to quantitatively characterize the nonlinear mapping mechanism between the thermal behavior of the gantry guideway grinder spindle and its resultant geometric deviations. A spindle rotation error analyzer is employed to synchronously capture the full-field thermal distribution of the spindle and the spatiotemporal evolution characteristics of the resultant thermally induced geometric deviations. The random forest and cross-validated recursive feature elimination (RF-RFECV) algorithm is employed to select temperature-sensitive parameters, decouple spatial correlation effects, and achieve robust extraction of dominant thermal influence factors. The feature-selected temperature rise data served as the driving signal, with axial thermal error designated as the prediction target, to construct a gated recurrent unit (GRU) prediction model. Bayesian optimization (BO) is introduced to adaptively search for optimal network hyperparameters, thus overcoming the local optimum constraints inherent in empirical parameter tuning. Experiments show that compared with GRU, LSTM and sparrow algorithm optimized GRU (SSA-GRU), the average absolute error (MAE) of BO-GRU model prediction is reduced to 0.48 μm (17.9%/82.5%/27.8% reduction), the mean square error (MSE) is reduced to 0.38 μm (28.8%/96.5%/46.3% reduction), and coefficient of determination R² = 0.9995, indicating optimal fitting performance. Comparative results demonstrate BO-GRU’s superior prediction accuracy and thermal error modeling capability. This framework provides an integrated data-driven and intelligently optimized solution for spindle thermal error compensation.