Yep, if not the coolant, then it's either Thermostat, Water pump or Fan. If you have not yet replaced under recall the "infamous" Siemens fan, then that could be a culprit.
Thermostat is less of an issue on our cars, since when it fails it gets stuck open, not closed. So if anything, the temps would read lower. I had two replaced already...
Water pump is another bugger. BMW may still have installed one with plastic impellers that would fail quickly with use. Though I thought they got over this already. My pump was replaced after about 5K miles in 2001.