Paper friction materials are used for a multidisk wet clutch as part of an automatic transmission. The performance of these friction materials is known to influence the clutch greatly, and this performance deteriorates due to frictional heat generated in the contact surface at engagement. Therefore, control of temperature in the contact surface is required. In this paper, we focus on the effect of oil flow on contact surface temperature, and we carried out a numerical simulation of the heat transfer. As a result, it was shown that the heat transfer by and conduction was dominant in comparison with the heat transfer by the flow of the ATF, and that consideration of thermal resistance by the oil is important to predict engagement face temperature precisely.