[@Keksalot] This is only my two-cents, in response to J's first point:

First off, besides area and time limitation, what about body limitation, such as a cap of how much heat he can absorb before he literally burns himself to ash? He's still a flesh and blood human being, not a humanoid inferno (for example, those with fire/lava/magma physiology). Also, [i]absorbing heat doesn't make him immune to cold[/i] - in fact, it's quite the opposite: he has to keep absorbing heat to keep himself warm - which is to avoid cold, so as J has said it's logical for him to be weak against Metahumans with water- or ice-type abilities who are capable of cooling him down and make him lose those "stolen" heat. In a way, he's somewhat similar to pyrokinetics that he's more resistant to heat but weak against cold, not immune - like, there's no way he won't get burned by a pyrokinetic spamming him with a barrage of lava-hot fireballs (he can't possibly absorb the heat that fast enough).

Sure, the whole absolute zero thing sounds cool and all, but for him to be able to perform such a feat is a suicide move - overexertion/overuse of ability will lead to ashing, which is death to any Metahumans regardless of their power. Yes, I saw the "theoretically" word, but heat is constantly generated in nature as long as the particles are vibrating and interacting with one another. In science, so far absolute zero can only be achieved under controlled environment, so realistically it's extremely difficult to do that in an open place like our daily surroundings where heat energy can travel around freely.

I'm not sure what scale you're using for the temperature figures, but if it's -90°F (-68°C) and able to absorb so much heat to reach that low in only a couple of minutes is kinda stretching the limit. I mean, imagine going from a normal room temperature of, say, 77°F (25°C) to -90°F in a matter of 2 minutes... Can you imagine how much heat energy your character has just absorbed into his [i]human[/i] body? 

Ok, maybe you can argue that he uses these absorbed energy to augment his body, but again, [i]he is a human, not a freaking god[/i]. Meaning, if you want him to be able to absorb heat that fast enough, then vice versa it's logical for him to lose that heat energy at a fast rate also in order to maintain his body temperature from overheating. Also, tissues can harden but they are still living cells not kelvar, so his enhancement doesn't make him bulletproof, just that a pistol shot won't be as painful as a snipe shot, for example.

Personally I feel that it's redundant (illogical) to have a "pocket dimension" to store the heat he has absorbed because you mentioned that his power is always active, always absorbing heat from around him but just that when he's passive it's at a slower rate than when he's actively taking in the heat. If you seriously want the pocket dimension idea, then you'll have to ditch the "always active" point. Either, or. You can't have both just because you need a backup plan in case he can't absorb heat that well in places with lower temperature (you even stated in your sheet that he has to always move to warmer places to maintain his power). See the irony there?