All have offered good suggestions and I don't want to cast aspersions on any of them or the posters, but these are my experiences both as an individual and in industrial applications.
Hot water does dry quicker and minimizes residual water in crevices, but it also can lead to flash oxidation. Ferrous oxidation is driven by time, temperature and concentration of the reactive elements. You increase the temperature and you can get "rust" almost immediately.
Heat accelerates the evaporation of the residual water that can be in the cracks and crevices of a firearm. But, often if we remove a dovetailed or other semi-permanently affixed part that has undergone cleaning with hot water or had heat used to accelerate the drying we find rust in the areas that are hidden.
Many people exclusively clean with an emulsified oil mixture like moose mild (Ballistol and water) because the oil is attracted to the surfaces, it coats them and prevents oxidation. Others, me included, use water with soap (hot or cold) and then either dunk in moosemilk or liberally spray them down as soon as they are pulled from the water. With a warm part the emulsified suspension is drawn into the cracks and before the oxidation takes place it gives you the protection you require.
Most and the quickest oxidation takes place not while wetted with water, but as the water is evaporating or in a humid environment. The oxygen atoms in the water are bound by the iron as the phase change takes place. You can do a simple experiment for yourself by placing a nail half in and out in a clear plastic cup of water. You will see spot oxidation very quickly above the water and then later dark oxidation under the water, but not immediately. Ultimately you get more aggressive corrosion above the water.
In gunsmith bluing operations (hot black oxide salts) and in large commercial operations the final step of most 5 step processes is submersion in a tank of water displacing oil. Some manufacturers of salts tell you to go directly from the cold water rinse following the hot salts and then to a water displacing oil. But I was taught this wasn't the best process, I was taught to go from the cold water rinse to a boil out tank of water (6 step process) to get all of the salts out of the crevices. How many times have you seen a blued firearm with "salts" coming back out of the crevices over the years?
I later changed the process for black oxide boil out to use a hot emulsified oil (very little oil in the mixture) instead of straight water. This minimized the need to rub down the surfaces to remove the oxide that was "remaining" on the surface. My theory is that the majority of this "residual" oxidation was actually a result of the boil out tank without a protective additive instead of true residual on the surface. With plain water you still got a nice dark finish, but when wiped down you got a brownish surface residual on your rags.
Just like the black oxide process you can get oxidation from hot water, remember heat almost always accelerates a chemical reaction. Personal experience and training has led me to believe the best solution is to displace that water and cover that surface before you go through that phase change of the water evaporating which promotes oxidation. Spray them down with moosemilk, then blow them off with compressed air and then letting them dry in the sun has been a recipe for success.
Regards,
Mako