The only think I can think of would be to attach a "hood" made of some loosely woven black cloth to the edges of the mask. That would at least eliminate the double layer under the mask.
While I don't have a Revan costume myself, I do have a very thin balaclava that I will use if I ever do make the costume. It's lycra/spandex type of material and just has one large hole for the eyes, so it can also be worn with the bottom portion pulled down under the chin. I use it for cross-country skiing as it is just thick enough to block wind, but doesn't hold in too much heat. I believe it came from REI, if that's in any way helpful.
This isn't the one I have, but it was the one with the closest type of fabric:
http://www.rei.com/product/801665/rei-performance-headliner
