the radiator cap was bad, the thermo sensor did not work properly so the fan did not kick in when it should.
Replaced both, big service, new battery. Not cheep but better than to get stuck in the dessert.
Still: there are vibrations (a grinding, as if something was not properly tightened or a shaft bent...?) that I can feel, especially when accelerating. It disappears when I pull the clutch or am in neutral...