Sounds like you need a new thermostat - they do fail. Get an OE one from a BMW dealer - most of the aftermarket items seem to be short-lived.
Easy job to replace - drain the coolant (and read up on the refill process), remove the radiator fan shroud and viscous fan assembly. Next, remove the turbo intake ducting and then you'll then have enough access to change the thermostat.
My car with the thermostat out...
If you have the water-cooled EGR, I think that can make access a little more tricky.
And you'll have a good chance to look at the wiring around the aux fan and AUC while you remove the radiator shroud...
