Interestingly, I haven't been able to find a real number for just how hot shell casings are when they get ejected. It's clear that they get hot enough to sting, especially in cleavage, but that's not really an adequate consideration. I can only speculate that, since ejected brass does not significantly oxidise, it is unlikely to be hot enough to set most matierals ablaze, even at high oxygen concentrations.
Certainly, there would seem to be considerable cooling during flight, since the walls of a cartridge are very thin and would cool rapidly.
Perhaps of more concern would be muzzle flash when firing from the prone position, although the flash duration is so short that I'm very dubious that solid materials would be affected.