Darkhorse, I agree...the temperature of a big old heavy muzzleloader barrel wouldn't change enough to notice it with that little amount of 'urine' in it, not much hotter than summer air temperature.
I clean mine in buckets of hot water that's at least 160 degrees coming out of the water heater and even after being submerged a few minutes, the water that initially leaks into the bore comes out cold...takes a lot to heat up that much steel.
Only supposition on my part of course, but with the constant need for water just to survive, I suspect their travels were always geared towards or included terrain that would usually have abundant water sources anyway...rivers, creeks, valleys, bottoms, etc
I know they'd think we were foolish to wish we could have lived back then, given all their hardships, but it sure would be interesting to "go back" for a couple years