Did I understand this correctly, the discussion is about soldering stuff to a rifle barrel?
Boring engineering stuff, originally published by the god of Mechanical Engineering, guy named Timoshenko, is that a 200F temperature differential is enough to deform steel. So if the solder is running 500F, and a wet cloth keeps the other side of the barrel down below 212F, you have a bent barrel. Not much. But still just a little bit bent.
I spent over three decades dealing with high temperature materials, nickel alloys that do their job somewhere between 1400 and 2200F. Most of the bent, broken, wierdly distorted pieces of nickel alloy I saw were from temperature differentials.
I found it almost impossible to convince a degreed engineer (yeah, well, I am one, too) that restraint of thermal expansion, or temperature differentials, can so distort metal.
Small farmers and skilled tradesmen did tend to understand, based on their experience.
But I guess I misread, and this thread is on the art of soldering thimbles to the barrel rib. That's just fine. Oh, yeah, and the cadmium was removed from silver solder because cadmium fumes are not so good for one's heart.