Oxpho blue is a form of phosphatizing, like Parkerizing. All the phosphatizing processes are done in water solutions that are below the boiling point. They have optimal temperatures that range from about 150 degrees to about 190, depending on the particular chemistry. Running cooler gives a thinner, finer coating, while running warmer gives a thicker, more matte result. I assume this would be true for Oxpho blue, as well.
Since the Oxpho-blue chemistry is formulated to work at room temperature, I would not heat the work unless I were going to dilute the product first. I have used cold blues diluted up to 4:1, but only at room temperature and only to slow the process to allow the coat to build without making gas bubbles that loosen portions of the finish. That said, a number of people do apply heat after the blue has appeared to help set it. I recommend you take some scrap steel and try any of these process alterations before actually trying them on your gun.
The advice to rub Oxpho-blue in is good, but realize the steel wool will consume some of the chemistry (unless used after applying the blue, as Pisgah described). I have had good success applying cold black to aluminum with an old toothbrush, which constantly removes loose surface color and puts fresh compound on the metal it exposes. You might experiment on scrap steel with both carding items to see what happens? Perhaps the color will be better with the degreased steel wool? I've never tried it with a cold blue, but do use it to card rust bluing between steps.
Rust bluing is slow (takes about a week to go through enough cycles to get solid color) but not difficult. You would need a water pan large enough to boil the rusted parts in to convert the rust from red to black, and a source of distilled or deionized water for best results. Rust blue will look darker and bluer than Oxpho-blue, which looks more like dark charcoal gray to me. Rust blue will be significantly tougher. Wearing off a bit too easily is one limitation of cold coloring compounds.
Brownells sells their own brand of rust bluing solution that isn't too expensive, and they used to have a policy of sending a copy of their printed instruction sheets out free for the asking. You could call them and ask for that if the idea interests you? The other day a fellow told me he rust blues using Brownells Dichropan bluing instead of a dedicated rust bluing solution. He finds it rusts well enough on its own if it isn't rinsed, and he thought the final color was darker, but I haven't tried it.
Regular rust bluing is about the color of old Colt blue, and has a slight luster to it rather than a high gloss. It is very handsome.
