Heat.

When rust bluing anything Winchester I don't use the slow process.
Below is a quick write up. Not getting into polishing, tools, rust solutions, etc. If you're familiar with the process, this will make sense. (Have a dinner date with my wife.)

Have water boiling, place barrels in boiling water after final prep.
Remove from water, blow crevices dry with compressed air.
Apply rust solution. If barrels are hot enough it should rust/evaporate almost instantly.
Boil barrels and then card.

Repeat as may times as needed. (Move quickly!)
I also keep a propane torch handy to keep things warm/hot but this requires CARE.
When done blacking and carding, coat heavily in non-detergent motor oil for at least 24 hours. Many oils have additives that will loosen rust blacking. As me how I know. shocked

The use of a heat source is VERY common. You can even find YouTube videos from inside Turnbull's shop showing his guys using this method.
That said, stick to the cold rust method if you are not comfortable with the process.

I had some great mentors who gave me hints & tips, but my process is not exactly the same as theirs, so this is just a guideline to be adjusted to your shop, tools and conditions.
More than one way to skin a cat.