You know, it just boggles the mind that as we sit here discussing a hobby that is technical in nature, based on a TON of scientific principals that we get the comments on here I have read.
Perpetual Motion? Really? I have to ask if you are trying to shine people on with that or you are serious.
Lets look at this from a different perspective. Heat up a rock to 200 degrees. Now remove the rock from the heat and put it in a metal can that is 70 degrees. The can will get hotter because the rock inside of it is hotter than the can when you placed the rock it the can. How does that happen? THe heat from the rock leaves the rock and transfers to the can. Simple enough.
Tube guts. Fire up your 3-500 and lay down on the key on FM. The Anode gets GLOWING hot. The filament is glowing hot. Glowing hot is over 1000 degrees for most objects. So where doe that heat go? Outer space, another dimension, how about into the glass envelope surrounding the tube and physically connected to the hot parts. Now when the fan is running, laws of thermodynamics tell us that air can act as a medium to transfer heat to.
But we need to understand something here. YOU CAN'T COOL AIR, you can ONLY remove the heat from the air, or anything else with heat in it, and move it somewhere else. Air conditioning in your home or car doesn't cool the air.. It moves the heat outside. Hence the reason the condenser outside gets hot and blows air hotter that the surrounding air, and in the winter, a heat pump will take the heat from outside and bring it inside to warm the house. But the scientific part of it remains the same. You remove heat from air, and transfer that heat to other air with air conditioning or a heat pump.
All that being said. Back to the can. If you put a fan on that can, you remove the heat from it that is being transferred from the rock so it doesn't get as hot as it would if you put the can in some insulation and didn't blow air on it. And that is what you are doing when you shut the fans down on a hot tube. The tube WILL cool off, but the outer envelope will actually get hotter before it gets cooler. Not because of free energy or some mystical nonsense, but because the tube contains things that are MUCH hotter than the envelope of the tube. And that heat will transfer somewhere. The only place it has to go is out of the tube, and to get there it has to go through the envelope.