Yeah, what's it's supposed to look like and how much area is it covering ?
Sometimes you can't avoid a "warm" material - sometimes a light one will just look wrong and completely different from how it's supposed to look.
Since cotton IS one of the "lighter" choices, I think this might be a case of just needing to not wear it, or wear it a different way or wear a cooling system if you think even cotton would be too hot.
Disclaimer : This post written by a Grumpy Old Man
Actually in the pipes:
- Remaking Ser Loras doublet.
- Luke Skywalker, A New Hope
- Wind Waker starter costume in swim material
Eventually: Paul from Dune, Faramir, Harry Sullivan