I use soap and water not so much for the powder fouling, but the patch lube. The same reason for hot water.
Put some butter on a dish and run cool water over it. Nothing happens. Run warm water and not much happens. Change to hot water and it comes right off clean. I get the same reaction with my patch lube.
I should add one thing that I didn't mention in my first post. I live in an apartment, so I clean in the kitchen in a bucket. At the strat of cleaning I turn one burner of the stove on. (electric) After cleaning and drying the bore with dry patches I used to worry about the breech be wet. So, I hold the breech end of the barrel over the burner to warm it up and dry any water left. Do that along with some Ballistol in the flushing water rinse has kept everything clean and rust free. I use Ballistol on the inside and outside of the barrel to prevent rust. I even use it on the stock to perk it up.
Then before I shoot I run an alcohol patch down the bore, then a dry patch. Shoot two caps, and i'm ready to shoot.
I don't use butter for lube, or bore butter - so no hot water is needed. Hot water causes flash rusting in many ML barrels.
I do use Neetsfoot oil and Trcks mink oil for lube- sometimes.
I rely upon the teachings of an established & world famous British Gun Making Company for this advice to use cold or cool water only for BP fouling.
Their formulate cleans all the fouling from my bores - hot water is not needed.
This particular British gun making company has been making FINE guns in England since the mid 1800's, muzzleloaders, single barrels, rifles and shotguns, double barreled rifles and shotguns, then breech loading BP rifles and shotguns, single shots and double barreled guns until into the 1990's, then into the 20th century with modern guns, single and doubles, bolt actions as well: guns that sell for hundreds of thousands of American dollars. They are Holland and Holland, & are still making guns today - not to be confused with the brand new modern USA manufacturer of ML barrels who used their name - you might ask, though, why! They are not affiliated.
They gave this cold water advice to a close friend of mine, who owned several of their double barreled black powder guns and who wished to keep them in top condition. Will showed me the letter he received from Holland and Holland on cleaning his most valuable black powder rifles and I follow and advise that direction today. In now 40 years since he received that letter, I've never had a spot of rust in any of my many/several muzzle loaders nor the ctg. guns in which I shoot Black Powder.
If your method works for you - GREAT! I will still advise what H&H said to use in valuable black powder rifles and shotguns.