Engine overheating when Idle

Hi,

My engine has recently begun to overheat whenever the car idles or moves at slow speeds. When I speed up and travel at higher speeds, the temperature starts coming down. It starts going back up again really fast at a stop light, etc..

I suspect this is a problem with the thermostat. During idle, there is not enough pressure from the radiator for the thermostat to regulate the coolant flow to adjust the temperature. Is this right? Do I need to check my water pump and radiator too? Will replacing the thermostat fix the problem?

Let me know.

Thanks.