Yeah the fact that it's spinning as much as it is would probably dissipate any excess heat that black paint would add. Lots of airflow. My guess, at least.
Does that happen often? When I pass by the wind farm every time I go to visit extended family, I don't think I've ever seen them stopped. Granted that's not often. I really don't know.
I imagine you'd place them in an area where there's almost always wind, otherwise you've planned poorly.