Thermal error prediction forms the cornerstone of CNC machine tool accuracy compensation. Addressing the nonlinear and time-varying nature of spindle thermal deformation, this study proposes a neural network-based thermal error prediction model enhanced with transfer learning techniques. The model integrates data from multiple sensors to feed into a GRU network, effectively capturing the temporal correlations between temperature fluctuations and thermal errors. Experimental results demonstrate a prediction accuracy of ±2.1 μm. The streamlined structure of GRU, featuring a gating mechanism and fewer parameters, enables robust learning of thermal error with reduced dependency on extensive training samples. This study validates the potential of deep time modeling for thermal error compensation in smart manufacturing systems.