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

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. 

I would suggest a hybrid amp that has the tube sound with much less heat. I own and am selling a Lector amp that fits the Bill 

Hi daveyf

You May want to explore a hybrid amp. This is an amp with a tube input stage so you’ll get the benefit off tubes such as the tonality and the timbral accuracy that tubes offer with a solid state output stage (class a/b would give off a lot less heat compared to a pure class a design). This way you get the best of both worlds with a lot less heat then a tube amp. In a tube amp, the larger output tubes give off the most heat.

There are are a lot of them out there. I don’t know your budget but PS Audio BHK amps are supposed to be very good and they always get good reviews. They are also not hard to find in the used market because they’ve sold so many of them. There are many others to choose from at all different price points. 

What I did is I bought a tube preamp which gives me that tonal color and “bloom” and accurate timbre that I can’t live without and I use a smaller solid state amp which to me sounds great. I have been very happy with that setup for years. Good luck.

Scot