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

Maybe become a nudist?

Heat is work and work is heat. 

Heat rises. I use a small silent fan above my tubes that sucks up and does not blow down. 

In winter tubes will help and in summer they will not so there’s a bit of equilibrium. 

Seriously a ceiling fan may be the solution for you.  

Yes-

As others have mentioned - Carver Crimson 275 -

https://www.bobcarvercorp.com/copy-of-crimson-raven

@austinstereo.  That is interesting. I am not concerned about the issue of injury, as I never let folk get near the tubes. Your client has a point though if he had little children or pets that could get injured!
The issue I brought up in my OP, has to do with the fact that the room size is also crucial. The smaller the room, the bigger the problem.
Some folks probably don't comprehend why this would be a problem, as they enjoy a large enough listening  room that a warm/hot amp ( heat wise) won't ever be an issue. 

You could consider a class D amp with a tube input buffer. The Purifi modules add very little of their own sound signature, but require a front-end driver board to provide some gain and impedance matching. There are a couple of companies that make amps using these modules (which are very efficient) that use a triode-based front end.

https://vtvamplifier.com/product/vtv-amplifier-stereo-purifi-audio-1et400a-amplifier-with-vtv-vacuum...

ATM makes an Korg NuTube based input buffer. I assume they make a complete amp that uses this buffer, but I don't know the model. The ATM buffer seems a bit pricey for what it is, but it might sound good. 

https://atm-audio.com/product/buffer-korg-nutube-for-hypex-nc500-and-purifi-audio-1et400-v2/

I haven't heard either of these, but have heard an amp using the Purifi module and it is very clean and detailed.

@jaytor Isn't the Purifi module a Class D module? I'm not really interested in a Class D amp, mainly due to the fact that all of the Class D amps i have heard are too sterile sounding to my ears. Even the 'best of class' Jeff Rowland models.