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A Lock-Up clutch is installed inside a Torque Converter to improve fuel efficiency. The Lock-Up facing generates heat, and the temperature of the friction surface rises during Slipping Lock-Up. The temperature must be maintained below the acceptable level for ATF (Automatic Transmission Fluid). Therefore, a prediction technics is required at the development stage. Heat flow analysis by CFD (Computational Fluid Dynamics) has been conducted to predict the temperature of the Lock-Up clutch friction surface. In this paper, the target is a Torque Converter with multi plate Lock-Up clutch. An appropriate boundary condition was applied to the flow simulation in order to set the correct total flow rate in the torque converter, and by verifying analysis results, it is confirmed that the prediction of friction surface temperature is close to the data from the experiment. In addition, it is realized that the flow rate has great influence on the temperature of friction surface.