When it comes to Macs, if Apple does a replacement, they actually replace with a new, current model that is equivalent to yours. I have never heard of them replacing with a refurb or same model as the defective one, even if that's what you request.
Since your Mac hasn't been diagnosed with anything, I can't see them replacing it.
The only things I can think of:
- Contact Apple and see if a product engineer will look at your console logs, sometimes an Apple advisor will capture information from your machine that downloads the console info to see if they can find what's causing the freezing.
- As someone else said, run the Apple hardware test, especially right after the machine has been overheating.
- See if the Apple Store will run their own test (I'm not sure what they use, maybe something in house or maybe TechTool Pro, etc).
- You could take their suggestion and send it in for testing. The risk is that they won't find it and will send it back in the same condition.
- Also, you can call Apple's executive customer relations. Call 408 996 1010 and ask for Executive Customer Relations (not service). They are usually pretty generous with the support they offer if you explain what's going on and at the least might be able to expedite the process for having your machine tested if you send it in, but from what I know, their internal guidelines are to replace after three attempted repairs or if there are other extenuating circumstances, or if the machine was purchased more recently.
Sorry it's not working well for you.