2001 Dodge Stratus 2.4L DOHC thermostat

I have an issue with my car that seems pretty commonplace amongst most Internet chat boards. I did want to ask the exact question here on the DodgeTalk board.

The issue:

The car seems to warm up only when standing still...in other words if I start the car and let it warm up, it blow warm air, but as soon as I start to move the temperature gauge drops and the air that is blown is cold/cool. This has been an issue since the engine light came on.

The issue seems like it can be resolved by replacing the thermostat.

I have questions:

First, should I take the car to the dealer and let the "machine diagnose" what the issue might be?

or

Should I just flush the radiator, and replace the thermostat myself?

You can replace the thermostat for around 10 bucks, new antifreeze another 10 bucks. Trip to the garage for this 80 to 120 bucks. Replace the thermostate and unhook the battery for a couple minutes. After you start it up the computer codes should be cleared and if there is more than a thermostat issue your light will come back on, but if it was just on because of not running at operating temature the problem is solved.

Thanks.