02 Neon Overheating

I have a 2002 Dodge Neon that has recrntly started to overheat. I can't figure out why it is overheating. It is very strange. If the engine is started cold, the car drives fine. I can drive it on the highway going 80mph for over an hour and then get off the highway and drive in stop and go traffic for over 30 to 40 minutes with no problem. Even if after driving on the highway, I let it idle in my driveway for 30 min, it will not overheat. If I shut the engine off for about ten minutes and drive it again, it will overheat within minutes. This pattern is very consistent. I have changed the thermostat. I am not loosing coolant. The heat runs fine so I don't think it's the heater core. The fans come on. The radiator looks good and is not blocked. Both of my radiator hoses are warm after a drive. Both of the hoses for the heater core are warm as well. I don't see any other signs that I may have a cracked head gasket. I don't know why the car runs fine when started cold but will always overheat when started warm. Any suggestions?