Here's why:
* Water pump failure: A failing water pump can't effectively circulate coolant through the engine. Once the engine reaches operating temperature, the demand for cooling increases. A weak or failing pump can't keep up, leading to overheating. The cold heater is a key indicator because the coolant isn't circulating properly to reach the heater core.
* Heater core failure: A failed heater core would typically result in a leak (though not always visibly external), potentially leading to coolant loss and overheating, but *usually* the heater would still blow hot, at least initially, before the coolant level dropped significantly. A completely clogged heater core *could* cause overheating, but it's less likely than a water pump failure given your other symptoms.
To confirm, consider these checks:
1. Check the water pump: Look for any obvious signs of leakage around the pump. If you're comfortable, feel the upper radiator hose when the engine is running. If it's not warm or is significantly cooler than the lower hose, that's a strong indication of a faulty water pump. A visual inspection might reveal a damaged impeller.
2. Check the coolant level: Ensure there is sufficient coolant in the overflow tank (when the engine is cold). Top it off if necessary but carefully. If you've lost a significant amount of coolant, you'll need to find the leak(s) before considering the water pump.
3. Radiator fans: Make sure the radiator fans are coming on when the engine reaches operating temperature. If they aren't, this could also contribute to overheating.
It's highly recommended to have a mechanic diagnose the problem. Attempting to repair a water pump or other cooling system components requires mechanical skills and the proper tools. Misdiagnosis can lead to further damage and potentially serious injury. The cold heater is a significant symptom and strongly suggests a circulation problem, making a water pump the most likely culprit.