You will just end up warping that barrel. Now way to heat it evenly, other than to submerge it in molten lead.
I watched a fellow do this one time with a barrel from a pre WWII, Colt SA Army revolver.
He put a length of baling wire throught the barrel and twisted a loop on one end.
The lead and pot were "PRE HEATED" so that the lead was in a molten state, before submergence.
NOW one very important thing. The pot needs to be large enough and the molten lead deep enough to accept the barrel "LENGTHWISE" so it can be submerged from one end or the other, so it can descend in a straight up and down motion and kept that way.
This allows the heat to be transferred evenly, so warpage doesn't happen.
The barrel needs to be left in the molten lead for more than a few minutes, to allow everything in the bore to come loose enough to swab out with a good stainless bore brush. The carbon residue, trapped with the lead, can be resistant to the process.
The fellow I watched do this procedure only did it with barrels that were in poor shape internally and leaded up very easily.
That particular barrel didn't have any finish left on it before it was dipped. I don't know what would happen to dipped in lead blueing.
He left the barrel in the molten lead for at least 20 minutes, suspended from a steel rod, through the loop in the haywire.
When the barrel was removed, it was immediately clamped in a vice with aluminum jaws and a tight stainless brush was passed through from the breech end a few times.
The bore was back to original metal and the pits were very evident.
The barrel was then thrown into a ''cooling'' box, filled with non flammable insulation. It stayed there until the next morning.
The barrel was reinstalled on the revolver and then sent to an auction house for sale.
OP, just get some Wipe Out Lead Out and follow the instructions on the bottle (yeah, I know, you're a man and men don't read instructions)
There are also kits available with brass screen patches to scrape the lead out and not harm the bore.