I found some cases that were cleaned a few years ago, and they had oxidized slightly. So I ran about 150-200 in a harbor freight rock tumbler with a pinch of lemishine and some coral wax car wash. 45 minutes later, they were clean and wet. Not really shiny, but clean. I used a 4 inch slotted drain cap with the slits in it to drain off the water, shaking the tumbler to try and get water out. I rinsed them a few times. Then I put them on a towel. Then I rolled them back and forth in the towel by holding two corners in each hand. I used a couple of 45 trays to stand them up. (like this ) I put a paper towel over the 45 tray to hold them in place, and the flip them onto a piece of 1x6. (The paper towel is between the upstanding brass and the 1x6. The case mouth is pointing down, and the primer holes point up.) Once they are dry, this is a great time to pull out the military crimps, if you are so inclined.
My house water has too much ammonia in it. (They call it chloramines, which is clorine and ammonia.) I clean that out with a zero water filter, and that is what I use to wash, but the rinsing was at the hose outside. So I wanted to get them dry quickly.
A harbor freight dehydrator will work. It does not heat up the brass much. So I would not worry about the heat harming the brass. I tried it, and it works ok. It does, however, cause them to tarnish a little while drying. If you are living in a very humid area, then you may need a dehydrator. I live in a desert, so I have very little humidity.
You didn't say whether you were doing straight walled or necked cases. Necked cases are a little tougher, because the water may be pooled up inside the case. And thus may require more work.
Overall, this process is very quick.
