Firstly have a look over at f650.com. As said. It's a commen issue because of the way the motor was designed.
Regarding the pump. There are 2 seals. One on the oil side and one on the coolant side. The cavity between them is drained with a little hole. You probably already know this. But less known is that BMW follow the manual which says to put grease in between which is stupid because it blocks the drainage of the cavity which means you have no warning. Another reason to do all your own work. But i'm not sure this is the problem because you'd notice your oil going bad. Could be the sensor if it's not really overheating. The guys on f650.com have possibly seen this before.
I know the cooking system is designed with very little tolerances and gaiters have been known to cause problems, though i've never had any issues myself.
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