During the engagement process of wet multiplate friction clutches, complex temperature and stress distributions are generated, which have a substantial impact on their performance and durability. Previous studies have not fully accounted for the thermal-fluid-solid coupling that occurs during the engagement sliding process, and they adequately considered the strength of the clutch hub and the structure of coolant inlet. Therefore, based on the theories of heat transfer, solid mechanics, and computational fluid dynamics, we established a thermal-fluid-solid coupling finite element model for a clutch system using an ANSYS Workbench and Fluent simulation. We analyzed the temperature variations and equivalent stress distribution within the friction pairs and fully considered the clutch hub strength and the oil-filling characteristics of the coolant inlet structure, thus enabling accurate predictions of stress and temperature during clutch engagement sliding. We observed that under the multifield coupling situations in clutches, the interaction among the stress, temperature, and flow fields occurred during clutch engagement. Sliding friction work was transformed into variations in temperature gradients, which induced thermal stress and thermal strain, while the coolant inlet structure was the primary factor resulting in insufficient cooling. According to these predictive results, enhancing clutch hub strength and optimizing the coolant inlet position effectively reduced temperature variations in the friction pairs, thereby reducing thermal stress. This research has been demonstrated to provide an effective foundation for health prediction in wet clutches.