Nice looking setup. Ah the old subwoofer in a cupboard - you are clearly torn on style vs substance!
Heat dissipation is an exact science and you would be able to measure the air temperature around the amp while running it at high load for extended periods. I suppose heat would be convected out of the front of a cubic space like that fairly well. It would come down to how much heat the amp generates and how well it tolerates being hot for long periods. You might end up thinking about fans and mitigating signal and audio noise from them in the long run.
Others will know more but I would personally be uneasy about putting an expensive valve amplifier on the same shelf as a speaker.