A natural fabric, wool blend is what good sports coats are generally made of. Or cotton or linen. Any good quality suit or sport coat material will work other than tweed or flannel. Something light and flexible.
1) Material. Not even 1% spandex, lycra, or polyester for me. It makes me too sweaty. Cotton, linen, and good quality wool are the materials I go for.
2) Lining. Unlined or partially lined jackets are going to be cooler. Even the lining material can make a difference.
3) Canvasing. Cheap coats have layers of material fused together with glue. This makes them hotter and less breathable. Good coats will be canvassed (you can feel the separate layers if you pinch the fabric around the lapel.
4) Feel. Soft and tactile makes or a more pleasant experience for my partners. My most breathable coat is a linen one, but it gets damp fast, so my current favorite to wear is 100% cashmere. Even though it's a bit warmer, it's pretty breathable, and the soft fabric stays dry on the surface. I also have a 100% cotton velvet, unlined coat that always gets compliments for its softness.