A hot barrel doesn't put the bullet in the same location (relative to the sights) that a cool barrel does. The main reason to let it cool between a series of shots is to keep consistent point of aim / point of impact relationship. But we are talking mm here, not inches, so probably not too much to worry about if you are not shooting in competition.
If you shoot really really fast you could get the barrel hot enough to "cook off" a round without pulling the trigger, or to warp the barrel as the metal softens... but it will start glowing and be too hot to touch before that happens, and you probably can't keep it loaded fast enough to make that happen. (machine gunners worry about this, but pistol shooters really don't need to worry about it).
Let it cool off from time to time while you reload magazines or visit with the guy shooting in the next lane.
As for cleaning, your owner's manual should tell you what you need to know. Disassemble the gun only as far as shown in the manual. If a revolver, you need to clean the barrel and the chambers in the cylinder. I use a plastic or bronze bore brush with solvent, give it about six good passes, then follow up with patches until the bore and cylinder is clean and dry. Examine the patches to decide when it is clean enough. They should come out pretty close to white (a light gray is usually okay as that color might be coming off the aluminum cleaning rod). Use a toothbrush to clean around the hammer, the trigger, and the mechanism that rotates the cylinder. You are making sure any grit or grime gets removed before it has a chance to gum up the works.
If you are shooting .38 in a .357 you need to make sure the cylinder's chambers get cleaned especially well, otherwise a buildup could cause problems when .357 cases expand into the junk left behind by the 38 cartridges and get stuck, making them hard to eject.
If it is an auto-loader, you need to remove the slide and barrel and any associated springs and bushings. Clean the barrel as above. Use solvent and a toothbrush to clean the inside of the slide and the rails it rides on in the frame. Wipe down the springs and bushings with a cloth. Use the toothbrush to clean out around the hammer and visible parts of the trigger mechanism. You shouldn't have to take all those mechanisms apart unless you've dropped it in salt water or something.
Wipe everything down and let it dry before oiling. Put a drop of oil on each slide rail (auto) or on the mechanism that rotates the cylinder. Put a drop on the base of the hammer where it pivots on its pin. You might have to use a long tube or let a drop fall off a toothpick to reach it. Put some oil on a cleaning patch and run it down the barrel and into each chamber on the cylinder. If you are putting the gun away somewhere, wipe the exterior down to leave a very light coat of oil. Go easy with the oil... too much just attracts grit.
Clean your magazines every once in a while too. Remove the bottom plate to let the spring out, wipe it down, oil lightly, then reassemble.
Check out this link:
http://www.kleen-bore.com/safetytips.html
