... and I don't see the difference in heat transfer from the brakes to the rim itself in standing still or moving.
The heat transfer from the brakes to the rim may not vary but rolling the wheel will cause a heat increase. Perhaps this is the issue and the reason the aircraft should remain stationary.
Try driving your car for a bit on cold tyres. Come to a halt without the use of brakes, feel tryes. They're warm - rolling friction.