In the evolving realm of precision machinery, paramount importance is placed on the efficiency and performance of transmission systems. A central role is played by gears within these systems, with their thermal variations and distributions during operation critically influencing the stability and efficiency of the systems at large. Despite the theoretical support lent by traditional thermodynamic theories and empirical formulas, their prediction accuracy is found lacking, particularly in the face of complex operational environments and dynamic changes. To address this shortfall, this study introduces an advanced thermodynamic model, augmented by the application of a Temporal Convolutional Network (TCN). The integration of these methodologies facilitates a comprehensive thermal analysis and prediction specific to gear operation, aiming to provide enhanced accuracy and real-time thermal data support. This endeavor is vital for not only understanding but also optimizing the thermal behavior of gears in precision transmission systems, ultimately contributing to the advancement of the field.