Anything you do to reduce the temperature inside a power amplifier will extend the lifetime of some components, most notably electrolytic capacitors. This becomes important sooner or later. FWIW, the interior temp I measure on my big Krells hovers in the 130s F.
The temperatures inside digital processor chips may not have so much to do with power amplifier temperatures.
As far as what to do, first, my larger amplifiers are all basically at floor level -- where the air is cooler. Being something of a "swap-a-holic", I've built dollies for my amps, with large openings on the bottoms. The bottoms of the dollies are essentially rectangular frames, and are three or four inches above the carpet, to allow air to flow in unobstructed. I would not want to introduce any fans for concern of acoustic or electrical noise.
Cheers.