1999 Ford Taurus overheating problems?

I have a 1999 Ford Taurus with the 3.0 OHV engine. Recently, it has been overheating, mainly when pushed more then normally. For example, we will be going down the freeway at about 75 for 30 minutes and the Guage will be fine until we park and shut it off. Then it overheats and the Guage is at the red. There are no visible leaks or hose damage and the heater doesn't blow out hot air. I changed the radiator cap. I'm thinking bad head gasket, thermostat, or heater core. Is there a definitive way to find it before the engine quits?

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