One foot pound equals about 1.36 joule, 0.32 calorie, or 0.0013 Btu.No.... this is not a ballistic pendulum. This is a bullet that strikes a steel target and falls inert to the ground with zero velocity, energy and momentum and the target is left standing. You are ignoring what happens to the bullet and the target. It takes a transfer of "energy" to deform both the bullet and the target. This is in fact where most of the energy goes.
We are not talking about 1 ft lb of energy, we are talking about 4800 ftbs. If most of that energy was transfered into thermal energy, it would blister your finger to touch the target or bullet. There is only a very slight amount of energy that is tranfered to thermal energy in this type of collison or when a deer gets shot. You will find zero data to back your claim.
4800 foot pounds equates to 6.24 BTU's not enough heat to matter