Amps that don’t impersonate space heaters.

Simaudio, accuphase or luxman(class a/b). I have both and neither run that hot. I live in Chicago as well. Stay away from pure class A. 

I also live in the Chicago area, and the amp I use that never gets more than room temperature is an Anthem P-2 you can play it all day and night at full power and it never even gets warm to the touch.

ADG monoblocks sound very good for the money and produce little heat… and come in a carrying case and look like tubes to boot. I’ve had them in my system. 

I used to run a BAT VK55SE amp and loved the sound, but couldn't bear the high temps in the summer. I picked up a pair of Atmasphere Class D monoblocks prior to last summer and haven't looked back. Much as it bothers me, I never put the BAT back in service during the 'dark season' as the Atmasphere Class D amps just sound too good to put on the shelf.

I'm running them with a BAT VK33SE preamp, into a pair of Raidho X1 monitors, in a studio-like (i.e. very near field) setup and absolutely love the sound. 

Per his comment above, I'm in the same camp as Ralph: The sound the Atma Class D amps put out has everything I need to enjoy hours of listening, deep into the music, and without fatigue. The fact of them running with virtually no heat is but a mere side benefit.

GanFet or Class A (sliding bias tech) SS amps