Water pump same old story
110K miles and mine went. 2006 E90 with the N52 engine. I ordered a pump and thermostat on Ebay. Euro Auto Works, and I got it in two days. 341 for the pump 68 for the thermostat. I spent five hours total doing it. I am not a mechanic but have always worked on my cars.
One tip is that the top bolt on the pump can be easily reached with a 4" extension on a flex head ratchet. It is strictly by feel with your left hand on the bolt head, guiding the socket, with the ratchet handle down through the frame.
The symptoms were all the same as everyone else, overheating a couple times. I did the purge cycle and recorder the pump using my iphone laying on the pump, and it was clear that the pump was trying to run repeatedly, but was stopping after 2-3 seconds. probably due to drawing too much current. When I compared the old pump to the new pump, the old one did not spin freely campared to the new one.