I managed to fix the coolant problem: What I didn't know is that the F650 has an air bleeding screw. The right way to refill the coolant system is: fill it up, bleed the air (on the right hand side of the engine block), refill, run the engine, bleed, refill, run the engine.... you get the idea.
Took about 30 minutes in total, and after a first test-run of about 10 miles in town everything seems good to go.
I also fitted some bits I had ordered from Germany: got a new metal chain guard from ebay (a good alternative to the more expensive Touratech aluminium one), and a 'Rallye front sprocket cover" from Touratech. At 51 Euros this wasn't cheap, but it's a handy thing to have: I can now fit my 'Loobman' chain oiler to the front sprocket, the sprocket is easily accessible for maintenance, and on a worn-out chain it'll protect the engine case (at least that's what Touratech say).
