If it never stops running then you should see a frost build up on the back freezer wall. The defrost timer should be shutting it off at least a couple times of day, if it isn't then the unit would stop cooling correctly and there ought to be a layer of frost on the rear freezer wall.

Make sure your condensor coils are clean. Try playing with different settings with your controls. Lastly it's possible the thermostat could be bad. Usually though, if it never stops running it will freeze things in the fresh food compartment. Below is the breakdown of your unit along with the thermostat listing.

Part number: AP2061750

Enviroment definitely comes into play, especially where your describing. I'm from FL, so I know what you're talking about. The good thing is even though it is running a lot, it really isn't gobbling up a lot of power. But you're right the new ones are more energy efficient.

I've heard the Government is going to be running another program where Refrigerators are going to be involved, similar to the car program. Might want to wait and see what the offer will end up being.