Just so I'm clear, you used more than one pipe cleaner to clean out the airway, right? It takes several at a minimum to remove tars, oils and gunk sufficiently. A pipe doesn't need several hours to cool off. It's usually good to go in a few minutes.
A pipe cleaner or two is good if its just cleaning between bowls of tobacco on a given day. But it's not sufficient for cleaning a pipe at the end of a day's use before setting it aside to rest and dry out.
When I'm done with a pipe for the day, I give it a thorough cleaning, The bowl is separated from the stem. I start with tapered bristle pipe cleaners, as many as needed to clear out the draft hole in the shank. When the cleaners show no discoloration, the airway is clean. I also double over several bristle cleaners to clean out the mortise thoroughly. After cleaning with the bristle brushes I use a couple of fluffy cleaners to soak up moisture, leaving them in the airway while I clean out the stem.
I'll wipe off the sides of the chamber with either doubled up pipe cleaners, or a wad of paper towel after dumping out the dottle. This improves the quality of the cake that you build.
The stem always gets cleaned out with alcohol and bristle cleaners with every cleaning. I don't want any sour taste coming from the stem. I may not use alcohol every time I clean out the shank and mortise, but I do use alcohol every time that I clean out the stem. That's a practice that I got from reading Rick Newcombe's book, In Search Of Pipe Dreams. When he showed me some of his treasures last week I was struck by how incredibly pristine are his pipes. They all look like they just come out of the display case.
If you're worried about getting alcohol on the finish, just clean your pipe with the shank pointed down while using the alcohol soaked pipe cleaners.