For using BC PlumBrown, you read correctly. The part has to be heated to about 260-290. If it is colder than that , the PB will deposite a layer of copper which you then have to sand off and start over.
If it is hotter than 290, the stuff evaporates much to fast leaving an ugly deposite that will leave a discolored area, no matter how many coats you apply.
The process I use is to completely degrease the barrel. Use rubber gloves so the oil from your skin does not contaminate the metal.
Heat the barrel. (do this outside. The stuff may not contain mercury but it's fumes can't be good for you.) I usually end up doing this in sections because it is too hard to keep the whole barrel at the right temperature.
Apply the solution putting most of your effort into the top and sides of the barrel . You can always go back and get the bottom which nobody will see anyway.
After the whole barrel is coated, wash off all of the crud using paper towels to wipe it clean.
Now, start over with the heating and applying.
It usually takes 4 or more coats to get a uniform looking coating.
After the last coat and wash, sit it in a corner for at least 5 hours.
It will look rather crappy at this point but heat it back up to about 160-180 degrees and apply a coating of linseed oil. This will darken the color and even out the appearance. (I have used Sheath to oil barrels at this stage and it worked OK to even out the color but the linseed will do a better job.).
Count on spending at least 2 hours doing this job.The heating, applying, washing, reheating takes time. Oh, you might want to practice up on your profanities. They help a lot when doing large parts like barrels.
Actually, I like this stuff, but find it works best on small things like lock plates, cocks, butt plates, trigger guards and the like.
These small parts don't show the uneven look that some of the larger parts have.
In all honesty, for large parts like barrels, the Laurel Mountain stuff is a lot easier to use and get a good looking browning.