It's a good question, but sadly the problem with anything lighter or more natural,is that once it is wet it stays wet, which isn't great for your guinea pig.
I did make a couple of cotton lined tunnels last Summer, but they got wet and smelly within hours and just didn't work.
You need a fabric that doesn't hold water, and most natural fabrics do.
I tend to use fleece tunnels or cuddle cups in the warmer weather so the piggies can always get plenty of ventilation, and can also choose to sleep elsewhere if they get too hot.