Over the years I have developed a preference for cloth.
I have found the biggest thing to make a difference is the width of the brim.

For the wide brim hats I also like the straw but I find they only last about a year before they have disintegrated.

I also found that the hats that are stiffened with plastics or other magic coatings uncomfortable.

If I was looking for a hat for the heat I think straw would be choice, second to my wide brimmed tilley.
I would be thinking of one of the cheap cowboy style ones that the Mexicans seem to like so much.
A full sombrero is likely overkill.

Another consideration is the inside band. I find plastic or elastic very uncomfortable. I like materials that soak up the sweat and help cool my head by evaporating it.