I know you're asking about sewing patterns, but just wanted to chime in that I made knitted and crocheted caps for my Mom out of that fluffy "eyelash" type yarn. They were really soft and she liked that the caps made her head look "fuzzy" because it was more like hair! :)

I think the double gauze would be lightweight, airy and cool. That idea was genius!

naNCY zIEMAN'S cAPS FOR ALL SEASONS AND FOR ALL REASONS. Great looks and easy to do.
Also check out chemocaps.com