I'm lucky not to experience this first shot/following shotsituation...I use TC and GM barrels, Natural Lube 1000, Goex BP, and patched balls...45/.50/.54/.58 calibers...temperatures I shoot in are from the teens to the high 90's with % humidity from the 40's to the high 90's.
I always sight inwith a clean dry cold barrel like I'll be hunting, but to be honest, apparently it doesn't matter using what I use above...which is good...becausethe last thing in the world I would want to do is intentionally foul a ML bore then go sit in the woods with it that way for hours on end...my two cents.