A clutch unit for use in the drive train of a motor vehicle between a drive unit and a transmission including at least one transmission input shaft. The clutch unit includes at least one wet clutch device that is provided with a plurality of clutch elements, in particular clutch discs, that are at least partially wetted by a coolant such as oil. The coolant carries away frictional heat that is generated by slippage between adjacent clutch discs during certain vehicle operating conditions. The heat absorbed by the clutch coolant is cooled by heat transfer from the coolant to a cooler that surrounds the clutch unit.