A friend of mine that gunsmiths uses a recipe of 50/50 (IIRC) sodium
hydroxide (Lye) and ammonium nitrate in a boiling solution.


That's "melting", not "boiling". Melting this stuff is bad enough! You
don't need the caustic soda, but you have to choose between a higher
melting point, or a lower eutectic melting point and a mixture that's
now caustic as well as a powerful oxidiser. I can't over-emphasise what
a fire hazard this stuff is - splashes onto a wooden workbench are quite
capable of starting fires.

So what do people heat this stuff up with, and in?
I'm looking at a ~20" barrel from a Hawken.

IIRC, for the original job I heated it in an oven, then wiped on the
bluing agent (Birchwood Casey something) while it was still 400 degrees
or so. Instant blue, but not as deep or as uniform as I wanted.