<p>Based on distributed fiber Bragg grating (FBG) temperature sensors and laser interferometers, this paper analyzes and models the comprehensive thermal positioning errors in closed-loop multi-axis drive systems. The study focuses on the complex challenges posed by the interactions of various types of errors under different drive systems and spindle heating conditions. By dissecting the problem into thermal drift and thermal positioning error components, followed by separate thermal error modeling, the efficacy of the proposed approach in error compensation is demonstrated. Notably, thermal drift exhibits higher variability compared to thermal positioning error, introducing greater modeling complexity and challenges. The research underscores the significance and complexity of studying thermal drift, emphasizing the effectiveness of closed-loop control with gratings in constraining thermal positioning errors. For the thermal drift issue, this study introduces the GGT model based on graph convolutional network (GCN), bidirectional gated recurrent unit (Bi-GRU), and Transformer architecture. For the thermal positioning error problem, precise Bayesian optimized random forest (Bayes-RF) model and a concise yet effective physical model based on grating thermal expansion are proposed. The introduced thermal error modeling methods have been proven effective, keeping the comprehensive thermal positioning error within a ± 5 μm range.</p>