I use a propane torch, and move it down the barrel, heating a couple of flats at a time, and then only for about a third the length of the barrel. While holding the torch in one hand I use cotton swabs with the solution to swab the heated sections of the barrel. Do this outdoors, or in a well ventilated room, as this stuff stinks when it boils.
I work down the length of the barrel concentrating on three flats- the top and the two sides are done first, just because- until I have done the whole length of the barrel. Then, using a rage to save me from a burn, I turn the barrel over so I can get to the next couple of flats, and work my way back from the hotter end to the cooler end where I started, then rotate the barrel and finish the final flats. You will have streaks of yellow residue, but don't worry about them. They will wash off with a good scrubbing.
If you want a dark plum brown stain, rather than the light rust colored stain some prefer, then instead of letting the barrel cool, and wash, heat up the whole barrel as hot as you can with that torch and spray WD40 or any other good grade of oil on the barrel. Some of the yellow residue will disappear doing this, but don't worry. You are going to repeat this a couple of time. The last time, I always wash off all the residue, and then heat the barrel up to spray it with oil again. I hang the barrel from a rafter in my garage for this last stage, and heat and spray the whole thing. I get a deep chocolate brown color to the finish, which I like and others have commented on pleasingly. I have been asked by many friends and other shooters who finised my barrel, and how I did it. Best wishes.
