I had heard in several places not to do it until the joint has cooled, and only to remove any residual flux? Something about the shock could cause cracks in the solder itself, or the brass fitting?
No, removing excess solder with a wet or dry rag won't cause any cracking of anything. Copper, brass and especially solder are all ductile materials. None of them are brittle enough to crack from thermal shock. The only reason people use a dry rag or dry paper towel to remove excess solder is that it works better than a wet rag or wet paper towel, NOT because of any risk of thermal cracking. GLASS will break from thermal shocking. Steel can also break from thermal shocking, but in those cases the steel is red hot and is plunged into an oil bath. Oil cools steel faster than water because of the envelope of steam that forms around the steel when it's plunged into water. You don't have those kinds of extreme conditions when you solder.
The reason they tell you to remove any excess residual flux from the piping after soldering is because soldering flux contains a chemical called
zinc chloride.
Zinc chloride is a metallic salt that behaves very much like an acid at the elevated temperatures that occur during soldering. Zinc chloride dissolves copper oxide (the brown stuff) very much more aggressively than it does bare copper metal (the orangey goldish coloured, kinda, stuff) so that if you didn't remove all the copper oxide when sanding the pipe end or brushing the fitting socket, the zinc chloride will dissolve the rest it when it gets hot. Also, if you didn't flux your pipe end or fitting socket immediately after sanding or brushing them, the zinc chloride will dissolve any copper oxide that forms on those surfaces before you get around to fluxing them.
When the solder melts and gets drawn into the joint by capillary pressure, the molten flux in that joint gets pushed out. Any dissolved copper oxide dissolved in that molten flux gets pushed out with it. So, what's left inside the joint is bare copper metal and molten solder; no oxygen atoms or molecules at all, which is what you need for a good solder joint.
But, keep in mind that zinc chloride is really only aggressively acidic at soldering temperatures. At room temperatures, it's "theoretically" acidic, but it'd take forever and a day to do any harm to copper pipe. Even on hot water supply piping where you might get 140 degree water temperatures, residual zinc chloride on the copper piping isn't really that much of a concern. About the only time where you really should remove any residual soldering flux is on hot water heating system piping where the water temperatures of 200 deg. F. are common. In that case, the zinc chloride in the residual flux MIGHT be acidic enough to etch the copper piping, thereby possibly weakening it. But, at the end of the day, and when all is said and done, I have never heard of copper piping leaking or being seriously damaged because the residual soldering flux wasn't cleaned off.
I use a popsicle stick to clean off any blobs of molten solder on the joints, and that works well too.
