Hello and well met, songbird.
Having met the designer of this well recognized Simplicity pattern, I have not used it myself. It can be made using Linen/Cotton blend fabrics. In the type of heat you are taking about, natural fibers will be your best bet. Medium weight should suffice. Stay away from heavier weight fabrics like Chenille Brocades, Upholstery weight fabrics, anything with Viscose and Polyester.
Chemises are best made in 100% linens. As well as Corsets. I use Cotton Canvas Duck for my under layers with boning, plus my fashion fabric and lining layers which are 100% Cotton. Same for my hooped slip or Farthingale. Wearing all Natural fibers for garb in any kind of heat will not only keep you more comfortable, it will protect your skin overall from evaporation. Though do stay hydrated.
If your faire is not going for full Historical accuracy, it should be permissible to wear high necked chemises with the neck open and gowns without sleeves. I have seen at faires like Bristol, where it can get into the upper 90's with high humidity where the Nobility are sans sleeves and opened chemises at the neck to be cooler.
Hats can be French Hoods, Tall Hats, Italian bonnets. Wear a snood or Caul of some kind with it.
A gown ensemble I made in 2015 from a medium weight Cotton Brocade and Silk contrast that I have worn in temps in the mid 90's. The sleeves are detachable as they hook and eye into place. I made sure I stayed hydrated, took my time getting places, and used a Parasol for added shade.
