I use Tubes that also run quite hot, the Amp's these tunes are utilised in are positioned in free space away from other Structures within the room.
I have in the past owned a Portable Air Conditioner Unit, that produced Icy Cold Air, this has been reserved for use when the External Temp's are getting up to the +25 Centigrade to help with sleeping. When using the room the system is set up in during these periods of high Temp's, I have never felt there was a need to run the Portable AC Unit during a listening session.
If increasing Room Temp's are a concern, as a result of a Tube Amp' being used, and a Cooling Device is at hand, cooling the Room in advance of the listening session is certainly going to cool the room and not impact on the Sound being produced.
My cautionary advice to an individual interested in using Tube Devices is no different to the advisories I was given many years past, which is to make sure there is always 'eyes on' the devices in use for the bulk of the time they are Powered On, and have a revisit shortly after being Powered Off. After approx' 30 Years of using Tube Devices, I have not had a concerning experience, only the oddity of a electrical glitch, a spent Valve or a blown fuse.