The problem is that they run hot as Hell, that's why they fail.
I'd call Apple Support directly rather than going through a third-party service centre as they have less power to get it sorted. Failing that, email Tim Cook.
That's an absolute joke then, if they're official they definitely know about the issues and they're just being stubborn.
You can email him at tcook@apple.com. Naturally be courteous and polite as a firm hand won't get you anywhere, but you will have to explain the situation that it's a documented issue and you're losing faith in Apple's support as they're not accepting there's a problem - despite you actively experiencing an issue and the temperatures are getting far too high.