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To design thermal fit parameters such as heating temperature and insertion force, it is generally necessary to conduct structural and thermal analyses, respectively. This study aims to build an integrated thermal assembly model to design the heating temperature and insertion force parameters simultaneously. A hierarchical multiple-kernel regression is proposed to map the two parameters and the thickness of the workpiece to the contact stress. Using the regression method, we can design the thermal fit parameters efficiently. The proposed model is validated experimentally based on two shaft-bearing assemblies. The results show that the model is capable of accurately predicting the contact stress in assembly. [ABSTRACT FROM AUTHOR]