Well, Gentlemen, I am a heretic. Two reasons.
#1 Grampa told me that he cleaned his rifle with cold water. As he never shot a breechloader until age 18 I figured he knew his stuff. Seemed to in everything else he said. Now those of you who are chemists will know that potassium carbonate, a.k.a. potash, a.ka. much of black powder fouling, dissolves slightly better in cold wather than in hot. The reaction of dissolving gives off a little heat. So it seems to me unlikely that hot water will clear out that fouling much better than cold.
Others who might know about corrosion know that chemical reactions go faster in hot water than in cold.
Translation: hot water corrodes steel (rusts) faster than does cold.
I used to clean my muskets & sporting rifles with hot water. They invariably got a flash of rust before I was finished.
Cold water, cold water. Dry & oil with your favorite Magic Oil.
#2 Salt rusts steel. Yeah, we all know thatl.
Soap - all soap, which really is not soap anyway these days - contains salt. One reason the soap makers put salt in the product is that salt does to soap much what it does to a garden slug when you sprinkle salt on it. Makes the soap (or the slug) flow better.
The Process Guys like this because they pump the stuff through pipes from vat to vat. I worked as metallurgist for a supplier of specialty heat and corrosion alloys. It was good for our business that Proctor & Gamble, and their competitors, liked to use so much salt. Meant we could sell really high alloys, stuff that makes stainless look downright wimpy by comparison.
Don't use soap. Soap rusts steel.
You like to think tradtional? Well, before Rachel Carson got people to thinking about ecology, soap had a little phosporic acid in it, and that served as a corrosion inhibitor. So if you supply of soap comes from the 1950's, go ahead and use it. It may have salt, but that phosphoric acid (used tp neutralize the lye) makes a good rust inhibitor.
Otherwise, Cold Water, Cold Water, Cold Water - no soap, not even Murphy's Oil Soap or Dove.
No soap. Hot soapy water will rust your rifle barrel.
Do oil it, of course.