Abstract: In the field of precision manufacturing, thermal errors of electric spindles are considered a key factor affecting machining accuracy. To accurately predict thermal errors, two methods are generally employed: physical simulation modeling and machine learning modeling. Because physical simulation modeling is complex and costly, machine learning modeling is often selected as the preferred solution. However, traditional machine learning modeling frequently lacks physical interpretability and exhibits relatively poor predictive robustness. To address these issues, a modeling method based on the probability distribution constraint of the generalized coefficient of thermal expansion is proposed to enhance model predictive performance. First, principal components are extracted from the temperature sequence, and the generalized coefficient of thermal expansion is calculated from the thermal error sequence. Subsequently, after fitting the probability distribution of the generalized coefficient of thermal expansion using a Laplace delta function, physical information is introduced into the Bidirectional Long Short-Term Memory(BI-LSTM) model training process through a combination of a physical loss function term and the traditional root mean square error loss function, enabling the model to learn prediction behavior consistent with the thermal physics of electric spindles. In this study, a single-step autoregressive prediction model is adopted, and to enable the model to reuse general knowledge acquired during the training phase while accelerating convergence and reducing computational costs, a “warm-start” strategy is introduced. Experimental results show that, after incorporating the physical loss based on the generalized coefficient of thermal expansion, model predictive performance on test sets under three different operating conditions is improved.