If I may add my two cents on the subject, I think you might be better served by including a weakness beyond going 'over-the-limit', for two reasons - exploit-ability and reliability.

If your only weakness is something that happens when your character overuses his powers, then that's not something anyone can actually use against you. Take, for example, our dear lord GM's character Meifeng and her primary weakness - electricity. That's an active weakness, something another character, if they knew about it, could actually use against her - if some dude rolls up with a lightning gun, she's up shits creek without a paddle. That's clear, it's exploitable, it makes sense.

Which ties into the second reason I've never really liked 'overheating' weaknesses in this sort of RP, which is the fact that it's not a weakness in practice at all. Be honest with yourself - are you ever actually going to say "Oh, well, I guess that's too much heat, he turns into a pile of ash and dies" ? No, nobody ever [i]actually[/i] overheats their characters, they just make DBZ-like declarations of 'tHe PoWEr iS bEcOMinG tOo MuCH! I aM SEConDs FrOm OVerHeATIng! WHaTEvEr wiLL I dO?', but they never actually cross that threshold, just teeter on the edge of it to highlight how rad and dangerous their character is. This isn't an indictment of you or me accusing you of attempting to cheat - I used to do it when I used that sort of weakness. Everyone does it. 

My recommendation, just make it so that he can't reach absolute zero, can't drain heat quite as fast, and give him an active weakness like, I don't know, maybe he's extraordinarily vulnerable to cold temperatures. Then, in my opinion, he'd be good to go, but then again my opinion's not the one you need to fuss about.