The system comprises an oil pump driven in conjunction with an output shaft of a transmission, a first oil path for supplying oil discharged from the oil pump to a lubrication system of the transmission, a second oil path arranged in parallel with the first oil path to guide the oil from the oil pump to a heat exchanger, and a valve inserted on an upstream side of the heat exchanger in the second oil path. The valve opens at a first set pressure to conduct the oil from the oil pump to the second oil path. The oil is supplied to the first oil path in a low vehicle speed area below the first set pressure, so that oil supply necessary for the lubrication system can be ensured. The oil is supplied to the second oil path in a high vehicle speed area over the first set pressure.