bro,
Last time I had the same problem. since I've got a bit know how on engine, I changed the thermostat. Found out that the thermostat locked on 'hot' position and somehow BMW ECU got a safeguarding or fail safe system some may say to cut off the power to starter solenoid when this happened just to ensure we won't overheat our engine. My symptoms were:
Engine temperature were slightly off than usual reads while running
Engine oil slowly over the period coming down, sign of vent or relief valve open during high temp
While car can't be crank, tried to pour some water on the thermostat's housing, tried cranked and engine started. Means thermostat seated after cooled down.
Well, this is just my experience. Dunno how Sifus here experience.
Adieu