question for the experts(overheat issue)

[X5SilverBeast]

My boss is borrowing a friends X and has a weird issue. I really didn't search, just figured I start a new thread. She tells me while driving with a'c on and comes to a stop, the temp gauge moves past middle, but not to red. Once the temp moves a bit, the truck shuts down by itself(saftey feature????). Let the engine cool off a bit and it starts right back up. I haven't had the chance to look at it, but my guess would be the thermostat or waterpump. Sorry for the vague info, this is all she gave me. It just sounds weird that when the gauge moves just past middle, the truck shuts down. I've never had this type of issue, so I have no clue. Let me know what you guys think. Thanks a bunch.

My boss just told me when she was driving this morning, a/c off sitting at a light, the temp gauge moved past middle, light turned green and temp gauge when back to normal. thermostat, waterpump, or air in system??