Fix the leak, fill the coolant, then see how the engine runs. If it overheats again in about ten minutes, try burping the air out of the system.
BMW is one of the three most customer-unfriendly manufacturers. Unfortunately you are stuck going back to the dealer for many repairs but any independent shop should be able to check the engine for you. Overheating is never good, but you didn't drive far enough to CAUSE further damage, and while it is odd the engine shut off, that may be not related to the overheating issue. I would not waste money yet on a lot of diagnostics when you already know there is a leak to be fixed. Start with that.
Tuesday, July 3rd, 2012 AT 12:29 AM