My '95 deville was just in the shop, I had to replace my compressor. When we picked it up our heat and ac was now working which it was not prior. On the first day the car overheated, not a problem we have previously. but the car did sit for a few months before we replaced the compressor. Could this be a problem with the thermostat?
The a/c system and the cooling system are two separate entities. A a/c compressor by itself should have nothing to with an over heating event in the cooling system, but then I don't know if the cooling system was compromised for some reason to change the compressor. The compressor is mounted to the engine and the serpentine belt goes around the pulley as it does the power steering, the alternator and water pump.
I don't really know how without seeing it, but possibly an over heating issue could have developed by not getting the belt around the water pump possibly. The only reason I throw that out is that you did not have a problem before. The compressor was replaced and the belt working the water pump could have a direct correlation to the over heating. Possibly, the belt installation has the pump running backwards and is not cooling the engine. Of course this is just a guess and I don't know, but it gives you something to think about.
Why would you need to change the thermostat out of the blue?
Here is your more dire problem: you have one of those finely engineered aluminum engines and this is not like a cast iron engine. It cannot hold up to any overheating and you are destroying the engine (it's melting) driving it overheated. If you blow out the head gaskets which you will, not worth changing because there are commonly more mitigating issues. All the engines in the junk yards have been over heated and they are junk as well, so you can't go used engine either meaning replacement will cost you more than the car is worth with a brand new engine. Stop driving immediately and have towed back to mechanic. Something is not right and all you will get is a very costly expense. Look in my archives for over heating on this engine. http://www.autotheftexpert.com