Overheating
Just had the same happened to my K1200S. About 11K mi.
Assuming you didn't blow a gasket, or cracked a cyl-head. My problem was the lid of the thermostat was blown open.
If you only refill in the overflow tank, that's not filling up the cooling system. These bikes use a vacuum pump, and a bleeding procedure (check a nipple on the water pump to purge air) to remove all air bubbles.
Very likely you have an air bubble in your system and it's preventing the pump from priming (get filled with water so it pumps). So right now, it might just be spinning in an air bubble, instead of pushing coolant.
Here's the cheap version (other than preferably going to a dealer and being robbed).
Take the thermostat lid off. Careful. The thermostat has a spring that eager to jump out. Make sure the thermostat is in place. It's very, very hard to put the lid back in place (o-ring and thermostat conspire against easy). This is done to check the thermostat, but also and very importantly to prime the pump.
If you don't want to do it, it's ok. Let's go further.
Open the radiator cap (use long pliers, it's hard with your hands). Very likely it's needing coolant. Fill up.
Fill the reservoir.
Start the engine. as it heats up, use a 11-mm wrench (I think it's 11). and open the water pump nipple to let air out. When the pump is primed and properly working, nothing but a steady stream of coolant should come out. If you have steam or air coming out, you still have air bubble.
Stop the engine. Tilt the whole bike to the right, and fill the reservoir. Make sure you want until the coolant is cool before you do this (about 20-mins). Start for about 10 secs with the bike tilted.
Tilt the bike to the left, and refill the radiator.
Now turn on the bike and purge the water pump until nothing but a steady stream of coolant comes out.
You can declare victory, when the temp indicator stays 2 bars below the mid mark.
Let me know if this helped. (check also i-bmw.com)
