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
The coolest amps are going to be class Ds no question but even they give off a little heat. Rogue's Hydra and Dragon are class D's with tube input stages. They are excellent. I have the hydra and it doesn't heat up much. The Sphinx and Pharaoh are integrated amp options from them.
AVMs Evolution A 5.2 is a hybrid Class D integrated amps with a tube input stage.
i am sure there are other Class D Hybrids.
These will be the closest you are going to get to cool tube amps if LTA is not an option. .
The coolest amps are going to be class Ds no question but even they give off a little heat. Rogue's Hydra and Dragon are class D's with tube input stages. They are excellent. I have the hydra and it doesn't heat up much. The Sphinx and Pharaoh are integrated amp options from them.
AVMs Evolution A 5.2 is a hybrid Class D integrated amps with a tube input stage.
i am sure there are other Class D Hybrids.
These will be the closest you are going to get to cool tube amps if LTA is not an option. .