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

"I don’t think you are ever going to find an amp that runs totally cool.   There is electric flowing through it and that is going to generate at least a little heat"     Correct!      All gain devices will generate heat, while in operation (none are 100% efficient), but- not all gain devices are defined as, "THERMIONIC" (requiring some heat to operate in the first place).      The operating parameters of one’s gain devices and how much output power is being called for, will determine how much heat finally results (aside from a filament’s contribution), while signal is being amplified.      ie: Some tubed Carvers = cool enough to touch / some FirstWatt (Class A, SS) = too hot to touch (for the sensitive)

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