It seems that I should turn the Kiln off at the end of the test firing. Typically, how soon after would I turn it back on to check the temperature and the ability to open the lid?

The kiln will automatically shut off the program after the firing. If you do turn off the kiln with the on/off switch you can force it to shut down but you don't have to. You can turn it back on anytime to see the temperature. If it is in the middle of a firing when you shut it off, and you don't shut it off for more than 30 minutes, it will resume its program.