Well, you might want to learn about
peristaltic valves for tyres. They do inflate the car while in movement. Another very common system used in intercity buses inflates tyres using a regular air pump on board. The first google I get on peristaltic valves is this:
http://mechsters.blogspot.com/2011/03/p ... em_22.html
Most buses in my country use the air pump system. It works pretty quickly.
A truly bad picture of the system used in buses. You can barely see the tube going to the green thing in the middle of the rim
They are very reliable, lightweight and
maybe fast enough. They are simple to control, I'd guess.
I guess the idea of heating the tyres with hot gas is not as useful as weaving behind the safety car (it's not that dangerous, I'd say and I find it kind of fun).
You might want to check the difference between temperature rising by
friction vs by
convection, conduction or radiation of heat through air.
Air is a very poor conductor of heat.
That's the reason why people heat wood by friction (as when you start a fire with a stick) while it is very hard to heat wood by blowing hot air over it.
Imagine me trying to start a fire on a piece on wood simply by
hanging it over the hot air that raises from a fireplace (without
contact with other pieces of wood). It would take an eternity.
That's also the reason why double window panes are so efficient at keeping your house warm.