A cooling system has a diverter valve to selectively control the flow of coolant through an internal combustion engine having a cylinder block with a cooling jacket and a cylinder head mounted on the block with a cooling jacket. A controller, responsive to the temperature of the block and the head, controls the diverter valve and a water pump to provide adequate coolant flow through the head and the block as needed to maintain optimal operating temperatures. After the engine is shut off, the controller continues to operate the water pump and a cooling fan to continue to cool the engine for a period of time.