I shake the cases around in a scrap terrycloth towel, set it on a flat surface and tap each case head against the towel to knock out any water held in the flash hole. I then lay them on some fresh towel and forget about them for three days. They are then dry.
If your water is hard and tends to make water spots, you can do a final rinse in distilled water before drying them.
There is nothing wrong with the oven in principle, but you have to be careful it doesn't go over about 450°F, even during the brief peaks when the heat source is on. That can weaken the heads, which you don't want to do.
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