I was home alone yesterday as wife was off taking care of some family business. At approximately 1030 I cued up 52 Ramones albums on Foobar2000 and let them play continuous and LOUD while I did some yard work out back and finished up the Hakko units upstairs. The system was cranked, media room windows were open as it was a warm day in Ohio, working outside the music was loud, upstairs working on the Hakkos the music was loud. The meters were swinging up to 1/4 of travel. Nine hours later after not touching the system I felt the amps for heat.
The fins were slightly above room temp, the output covers were warm, the transformers were warmer, and the top cover plate was the warmest. But nothing was hot.
To improve the cooling, if needed, maybe more holes or slots in the top and bottom plates are required. I can envision a steel mesh with a frame.
Perry recommended a nice fan unit some time ago that sits on top of the amp and blows upward. Rather than more air on the fins, I think cabinet ventilation may work better.
But then, if it's rack mounted, choices are limited.