You don't need to approach the main gear to tow the airplane, just the nose wheel, and I don't see the difference in heat transfer from the brakes to the rim itself in standing still or moving.
At the first sign of deflating they can always stop.
My scenario is the case in which you create serious problems to the airport in leaving the ac stuck where it is.
What about stopping in the middle of the runway and shutting down all engines?
The result, airport closes!
Anyways, that was just a guess as we all lack actual experience over this matter.
Thanks