I have a regular sport coat made from a silk/wool blend, and even though it's a fairly light weight material, I find that the silk/wool blend is an excellent insulator and it's actually a pretty warm jacket. I don't wear it much in the summer time.

I'm intrigued by the linen kilt jackets.

The museum gift shop offers jackets in a light weight twill wool (10 oz weight). I find that it is a bit cooler than the typical barathea wool (which is a 13 oz weight), and definitely cooler than tweed. It does wrinkle more easily than the barathea or tweed, though not excessively so in my experience.