Bad drum, good gear. Good drum, worn out gear. So you buy new rivets to combine the good drum with the good gear. I suppose you turn the rivets orange and mash them in the holes, then cut them flat in a lathe. Is that correct?
Yep, I insure alignment by screwing (bolting) the two together in all holes and removing one screw and nut at a time to install the rivet.
The two drums I have done, did them cold. Put the rivet in, placed on bucking bar and peen into place. Not all drum rivets are the same, there are long and short. The long ones I would use for replacing a full set, the short ones for just replacing one or two. When installed the short ones just fill the recess with not much above the working surface.
The rivets are very soft, I do mine in the press.
I bolt the drum to the gear and check runout before pressing the rivets one at a time in the press. Then cut flat on the lathe.
I shoot them cold with a rivet gun. Then face them off flush on the lathe. The steel rivets are not too hard until you shoot them. I don't think using heat is a good idea, the rivets would remain soft.