I have had some of the same things happen to myself, unfortunately they were a little bit of different situations. I think that my input will help you. I have learned that if you do an extremely good job of getting all of the bubbles out of the system, and then top up the expansion tank (filled to the top, not the recommended max mark) when the coolant gets hot and expands it comes out of the radiator cap, because it has nowhere to go. Their is just too much coolant in the system. I also found that after it lets this little amount out that when you check it at the cold temperature the level of coolant is then pretty close to the recommended coolant max line, and then it does not leak again. The reason why I, you , or Motorwerks would fill it up to the top is to compensate for bubble that are purged from the system while driving. What I would do, if you have not done something else already is wait till the engine is stone cold and see if the coolant is actually low. If it is not drive it and inspect again.

This would not fully explain the temp swing though. I also remember from cars built in previous years that some of these cars had bad water pumps to where the impeller (the thing that pumps the fluid) slips on the shaft driving it. So what happens then is when the car is at idle speeds then the pump is not pumping as much fluid as it should, then at higher rpms the fluid gets pumped more. But then you also have the other factor to consider is that an idling engine produces much less heat than an engine trying to push a car up hill. The only real way to check the water pump is to pull it out and see if it is properly attached to its shaft. But like I said before I only saw this in previous years to your car, and not on cars built around 2000.

My final thought is that you have a sticking thermostat. This thermostat will move then stop where ever it pleases. The only good way to verify this is to replace the thermostat. Yes I have seen thermostats go bad shortly after cooling repairs.

I have yet to see a BMW radiator not cool enough with out the presence of some sort of "radiator stop leak" in it. Another thing you may want to check is too see if the radiator has good air flow. Make sure their is no dirt or contaminants in the condenser or the radiator restricting air flow. If you do not see anything physically wrong with the radiator, then I would just try the thermostat. Another restriction you may have would be in the heater valves if they are not working properly. If you can blow really hot heat out of both sides of the heater I would think you would be okay. If you still have the same issue see if you can pin point at exactly when the engine overheats, it may be a fan clutch, or and auxilary fan issue.