Mark,
I wouldn't want to recommend anything that would mess up your gear, but I would think your player would engender similar (i.e. minimal?) heat as the Ah! player. The metal top gets warm but never hot--pretty much the same with or without the damping.
BTW, I didn't end up covering the ENTIRE top of the case. I covered the sides first but found that putting Dynamat all over the underside of the top
damped the sound TOO MUCH, muddying things and making it a bit lifeless. Eventually, I ended up with several 3" strips running front to back.
What if you left the area directly over the tubes uncovered??? The tubes could warm the metal, and the metal could dissipate the heat kinda like a heat sink????
Also, I have other tube gear (BAT phono & BAT pre) that runs very hot. I wouldn't even THINK of putting Dynamat even close to that gear; of course, the BAT stuff is built like tanks so I don't feel much need to tweak.
Hope this helps,
Tonto