I just use some bricks, the kind with the holes in them, and place them on the bottom. Traps have no direct contact with bottom of barrel.
Heat, even at 212 degrees, will affect the temper in steel. It may be a small amount, but it does have an effect. After many years of trapping and treating traps, I do not feel that it is enough to worry about.
Something that I believe affects the temper even more is age. Over time the steel just gets weaker, more so with coil springs than long spings; especially the smaller (#1) coilsprings. As these get weak I will replace one sping as this seems to power the trap back up to where pull outs are minimal. My #1's are in need of a new spring in the next few years, the second time since they were bought almost 30 years ago.