Disconnect or turn off the ice maker and see what happens.

I assume the compressor runs constantly.

Here is a link, check out #20 re: the example pictures at the bottom
http://www.applianceaid.com/refrigerator.html

Just a follow-up...

I had the repair man here this morning for 3 minutes. He listed to me and the unit and said "Go buy a new one. It is leaking freon.".

I knew that, but guess I needed to shell out $85 to hear it from the expert. It's too bad i could not get that kind of technical opinion from somewhere cheaper. I told him all the same information I presented here, he listened to the unit, and then came to the conclusion that it was leaking freon. (It makes sense as that is the only other variable. And, there is no way to check for a freon leak in a refigerator or freezer - in case you want to know. It is a closed system unlike your car's air conditioner.)

Also, a friend of mine had the exact same unit and it did the exact same thing once the thing got to be 6 or 7 years old. He just tossed it and got a new one. He saved the $85.

So, I am writing this to help any others out there - if your Frigidaire fridge starts to get warm and all the parts are working normal - its a freon leak. Save the $85 toward a new fridge.

Good luck.