To address the growing demands for precision machining, this paper proposes a novel thermal error compensation method for slant-bed lathes that combines mechanism-based thermal error decoupling methods with differential equation thermal error models. In the first step, the approach primarily decouples thermal errors of the slant bed lathe into component-level thermal errors through a movement measurement method improved on the basis of the experimental setup in ISO230-2 standards. Based on the thermal errors at the level of components, the method further decouples component-level thermal errors with the help of differential equations. The differential equations explicitly model distinct heat sources, including spindle rotation and feed motor operation, enabling precise decomposition of their individual contributions to overall thermal errors. To validate the robustness of the thermal error compensation model, an experiment simulating real processing was conducted, which emphasized that these models achieved a significant improvement in the experimental results by up to 50%. The mechanism-driven approach not only designs thermal error compensation models of the slant bed lathe’s main components but also provides a unique insight into thermal error origins through the thermal errors decoupling method.