Interesting thread. This subject...heat..is one that many a'philes should consider before purchasing the tube amp with multiple power tubes, IMO.
BTW, BAT is one of the worst offenders in this regard with their tube amps. ( Not saying their ss amps are). A good general rule is to look for an amp that is lower powered and has as few power tubes as possible. Fewer tubes= less heat. Plus, IME, the lower powered tube amp most time sounds a lot better than its higher powered brethren.
To the OP, depending on budget, I would suggest the new CAT JL5 Black Path amp...a superb peace that doesn't give off too much heat; or again if budget allows...a Jadis JA30Mk2, which is the amp i am currently using and it is magic.