When an engine is cold the thermostat is closed and water doesn't circulate through the radiator but only within the engine block. There is usually a bypass hose or pipe that allows this to happen. So, even when the thermostat is closed, water is still being moved by the pump... but only within the engine block. When the water becomes hot, the thermostat opens and the hot water is pumped through the radiator where the heat is transferred to the air. If the water gets too cold, the thermostat begins to close again, cutting down the flow. Inversely, if the water gets too hot, the thermostat opens all the way so more can flow though the radiator.