B/C plum Brown needs to be applied to metal that has been heated to about 280 degrees F. This is higher than the boiling point of water( 212 F.) but far below the temperature steel needs for tempering, much less hardening.
I hang barrels from the tang using a coat hanger thru the tang bolt hole. Then I heat from the bottom up. I apply the Plum Brown using Cotton Swabs, balls, or even q-tips, depending on the size of the metal piece to be browned. SLOP IT ON. As you finish with the muzzle, raise your torch up and heat up the next 6-8" section- which already has a head start when you heated the section below it.
The PB will sizzle and steam- and you want plenty of fresh air, and some kind of breeze- natural, or from a fan blowing the fumes away from your nose and face. Wear eye protection, and wear at least one of those light, styrofoam mouth protectors.
Wear some kind of glove to protect your hands from the acid. I put newspaper on the floor of the garage to catch the drips- and there are drips as I put more and more solution on the barrel as I go up from the muzzle to the tang.
I don't worry about my coat hanger, BTW. I don't prep it to receive brown solution, I don't degrease it or remove fingerprints from it. If it browns, fine. If it doesn't, fine, too.
Let the barrel cool, and when you can touch it with both hands, take it out into natural light to check all the surface to be sure you have covered it all. If not, take it back in, heat it up and cover those missed spot.
I got a nice chocolate Brown color using Plum Brown. After washing off the yellow/white scum, under the kitchen faucet, and using liquid dish soap to help clean off any fingerprints, I dry the metal, and then take it back out to the coat hanger. Once hung, I heat it up again- this time with long sweeps to heat the entire barrel(s)--- and then I spray it with WD40 and let the oil sizzle, and burn, and smoke. Until the barrel cools enough that the oil sits on the metal wet.
I found that by "burning" oil into the heated metal, it helps SET the color of the Brown, and Darkens it somewhat.
The Brown I have on my Dbl. shotgun has proven very durable, resists scratches in the field well-- better than any blued barrels I have---- and the color has remained that wonderful Hersey's chocolate brown now for more than 30 years.
The best part about heating the barrel FIRST, is that the browning solution works instantly when its applied, and there is NO wait time to determine what color brown you have, as with the room temperature products.
There is NOTHING wrong with the finish you get from the "Cold" brown solutions. It just takes more time to get there.
I think using Ammonia to neutralize acids is much faster than using Baking Soda. Have done both, and the processes have been adequately described above by other members. They both work, when used properly. Ammonia is pretty darn cheap.