I used my TA-15 head last night at a gig in a relatively cozy venue and yes, the amp runs hot: after the show I turned the amp off, let it stand for a few mins, then put it in its bag but left the bag's top open to let it cool further for probably 20... then I drove home (approx half an hour)... taking the TA-15 out of the car the bag was still warm, over an hour after it was switched off.
Also definitely watch out for getting any skin grease or sweat on the Platinum Pearl finished parts when it's hot because they do leave permanent (and I mean permanent) tarnishing, I had to have mine refinished it looked so bad.
Spectacular sounding amp though, if a bit noisy in higher gain modes, even though I use a Lonestar as my main amp I actually can't say which one I prefer playing through... compared to the Lonestar the TA-15 is just so damned accessible: it takes me seconds to get the TA-15 dialed-in for the venue, while my Lonestar can be much more fussy to get right.