I am guessing but think the recoil is counted in bbl heating. Case, chamber & bbl mechanics are reasonably easy to calculate, don't expect me to. Expansion takes energy, relaxation doesn't. Friction is calculated from coefficient of friction, yes it is heat but not that much and part of the heat is in the CB. In the context of this thread, we want proper pressure to get all the energy out of the powder without breaking anything. The time curve is important to keep acceleration increasing until the end of the bbl. Bbl temp is a function of bbl cooling and rate of fire. Thermal expansion of copper is really large.