How to make a cloth brim hat?
I have some experience with canvas hats.  I owned a Real Deal (hatmaker from Brazil) for several years. They're made from old canvas tarps, like the ones used to cover truck payloads.

Canvases has its advantages over felt.  It is slightly more breathable, and wicks moisture away a little bit better.  It's a marginal improvement over felt.  The greatest advantage is in durability.  With reasonable use and care, canvas will last for years.  Mine survived about 4 years of heavy abuse.

For heat control, eyelets will be helpful, especially high up near the top.

To help the top of the hat keep it's shape without making it too thick, there's stuff called boning that is used in fitted dresses and corsets.  Its a thin plastic mesh that adds stiffness without adding significant weight.  Asking around at a fabric store will put you on the right track.

Perhaps the easiest way to help the brim keep its shape is a piece of wire.  You can cut it to fit and then secure it to the edge of the brim with bias tape.  To keep the tips of the wire from poking through the tape, you can tie them together with dental floss,  a heavy dab of epoxy or if you have the ability, welding the tips together.