I've mentioned my 'Buff' tube scarf a few times, well that's a brandname, there are other versions as well. They are also advertised as "multi-functional head(or neck)wear" which is a bit more of a mouthful. Basically a tube scarf is just what it sounds like, a tube of light knit ("seamless microfibre") fabric, if you believe Buffwear's advertising they are quick dry and fluid wicking, keep you warm, sun protect, in fact do almost anything except cook and clean.
I LOVE my tube scarf, and am most often found to be wearing one when out training. Under the cycle helmet they don't seem to overheat but do keep the sun away from ears and the back of your neck, and in the rain and wind they help keep your head warm. I use an ordinary tube scarf under a sunhat for running in the cold and wet, but have one which has a cool little visor sewn into it which I use by itself for running in the heat. They go through the washing machine a lot better than your usual sunhat which is an advantage, you spend money on a hi-tec go fast sunhat and the thing gets grotty pretty quick because they dont stand up well to a good scrub.
Of course it seems there are lots of ways to wear a tube scarf, I'm a bit boring, choosing only Sahariane, Do Rag or cap usually, but some people are apparently endlessly inventive.