So long as the gear does not reach the point of glowing orange or hotter the temper should not really be affected. FWIW, 400F is plenty hot enough to expand the gear and not affect the temper.
I also agree with the general consensus that something is waaay wrong here. The gear ID is just too small. If you install it by heating the gear that type of installation is called an interference fit. You will need to heat the gear again to remove it in the future. Not exactly an easy thing to deal with if the crankshaft seal needs replacement in the future. The gear is supposed to be easily removed with the kit supplied puller all by itself.
I recommend getting to the bottom of the problem and fixing it properly, not using band-aid procedures as a get around.