Are there any tube amps that don't give off any---

I have a small integrated amp with 6C33C that put out a lot of heat and I biased these low, to the point that the entire amp innards get very hot, I set a Noctua silent fan underneath which helps with the heat but in the OP's case will only move the heat away from the amp into the room possibly making it hotter, I found a company which specializes in all these cooling solutions ACINFINITY you might be familiar with, like others have stated it may be easy to run a duct to the outside or other room with an inline fan, these are supposed to be quiethttps://www.acinfinity.com/duct-fan-systems/
32 dba is the equivalent of a quiet rural area so it should be pretty silent
Just my 2c

Hi Ralph, what happened with your prototypes? Any closer to your class Ds?

Yes. We've continued working on the design, hammering out details. Recently that's turned to the power supplies, since the entire thing has to be protected against shorted speaker loads and the like.

To avoid the heat of a tube amp. I guess your only option is to get a small amp and efficient horn speakers. I just auditioned a small Boyuu Reising model 100 amp that sells on Amazon for $400. It was really well built, sounded excellent but just didn't have enough power running two EL34 tubes. I matched it with some 90db Triangle Bro 3s and at 3 o'clock volume, it just was too soft for my 15x17 room. If you wanted a bargain system, combining this amp with some Klipsch M 600 speaker would be a nice setup for a  small room. I've seen these speaker on sale for about $400. Nice reasonable setup that will play much bigger than one would think. I did return the amp in favor of a Muzishare x7 with four KT88 tubes at 45 watts. 
Yeah, I know people like to gripe about Chinese stuff but look around. It's everywhere. You want an American tube amp, just pay for it. 

look for a tube hybrid if you are concerned with heat

Someone else has probably already suggested this but why not get a tube preamp and a solid state amp? The small tubes in a preamp will not produce much heat and when combined with a non-class A amp should give you the best of all worlds. Some of these preamp actually totally enclose the tubes. Something like the Schiit Freya with a good sounding amp should do it, I doubt that most class AB amps would add much heat, they may run slightly warm but it shouldn't be a problem in my experience. If you really want to kill the heat, class D is an option as people have reported but for me, I seem to be sensitive to their sound and I don't like it. Even the well regarded Rogue Sphinx 3 is a tube integrated with a class D amp and I passed on it. I understand some of the higher priced Parasound amps are well regarded. Schiit has a reasonably priced AB amp but you want to avoid their Class A Azir (?) amps for heat. My Schiit Raganok 2 is class ab and while it gets a little warm. Not an issue with me at least. 
I have read great reviews of the Brooklyn Class D amps so do your homework, get a 30 day or 60 day return on the amp and go for it.