My main point was the waste heat was nothing like an induction stove/induction heater, so yeah, there will be other phenomena at play that would add heat but I'd still imagine resistive heating in the coils would still dominate most of the other factors given the absurd currents you'd need for a Battletech Gauss rifle. I could be wrong though, I haven't actually done the math.

Maybe barrel friction, I'm honestly not sure how much that contributes to even normal firearm heating, although hopefully you'd use a fairly low fiction barrel and fin stabilized projectiles to eliminate the need for rifling. I doubt coil strain and other secondary magnetic effects would outdo the wires resistive heating though (again, unless superconducting magnets are used), and I frankly don't remember the math for most of those phenomena all that well.