Why is the car overheating when there is no visible leaks?

It could be many things BMW car is very sensitive to work. check your coolant level,hoses maybe has leak and the coolant recovery tank maybe has crack check that too. check your sensor, check your radiator fan if its working correctly.

Sounds like lack of flow because of air in system or pump not running. Did you have an overheating problem before?

You have to bleed the cooling system. I think the bleeder is right next to the filler. Looks like a cross. Start engine, loosen the screw, and fill when needed.