I’ve cooled pottery both ways. As you witnessed with your casserole mishap, there’s a huge risk when rinsing due to thermal shock. To be honest, we were a bit impatient and wanted to go kayaking so I sprayed my pot down 
which also stops the glaze from reacting to the environment any further.
We have a small kiln at home, but I’m a full time high school ceramics teacher and have access to their equipment. You can see my Ceramics Classroom here.