There are a couple directions you'll always be able to make the assumption that you don't need thermal masking in, though the vehicle would have to be able to determine what directions those are on the fly. For example, depending on the theatre and operating parameters, you may not need thermal camouflage from the sky.
Actually, there are no such directions in tank combat. If you do that, then you're playing a lottery with your life at stake. What if an enemy tank gets behind you, where you not expect it?
Depends on what sort of cooling system or just how well the material can disperse the heat
The other question also remains: Just how much heat is produced in the first place?
Guns can get really, really hot. M1 Abrams engine runs hotter than a Molotov Cocktail can burn. The answer is, a lot.
If you look into hard sci-fi stories, radiating heat in space is a major problem, since space isn't a good heat conductor. Air is a much better one, but this technology restricts it's use. My concerns are about how the vehicle would be able to get rid of this heat without messing up it's stealth or changing it's interior into a sauna. Getting rid of heat is actually a major technical problem in a lot of machines, thermodynamics are not very forgiving in that matter. (just look how elaborate the cooling system in a high-performance computer can get, or in a modern car).