A cooling system has an engine heat exchanger in thermal communication with engine oil in an engine. A transmission heat exchanger is in thermal communication with transmission oil in a transmission. A pump has a pump inlet and a pump outlet. A valve assembly is in fluid communication with the pump outlet and has a first and a second position that at least partially establish different coolant flow modes through a plurality of coolant flow passages. The valve assembly has a first inlet that receives coolant that flows from the pump outlet, to an engine inlet, then through the engine to an engine outlet. The valve assembly has a second inlet that receives coolant that flows from the pump outlet and bypasses the engine. The valve assembly has a single outlet that directs coolant flow to at least one of the engine heat exchanger and the transmission heat exchanger.