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The Thermostat is the brain for the cooling system. It senses the temperature of the coolant and allows the fluid to exit from the engine to the radiator. The Thermostat controls the temp. in the cooling system. Thermostats are rated at a specified temp. usually between 180 and 195 F. When the engine is cold the thermostat is closed. Once the engine reaches the thermostat rating the thermostat opens. Thermostats can fail open or closed. If the thermostat fails closed you are going to run hot, overheat. If the thermostat sticks open, you coolant will be cooler which can affect your dash heat.
The water pump is attached to the engine block. Its purpose is to keep the coolant circulating. It draws cooled coolant in from the Lower radiator hose and pushes through the engine. Water pumps are designed with a Weep Hole, this hole is a signal that the internal seals have failed, when leaking pump must be replaced. A failed pump would also cause overheating.
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