Personally, I think a single breasted blazer is a better style for the heat but men who prioritize stylishness over comfort should consider the 4x1 double breasted blazer for summer.
A 4x1, or 4 by 1 if you will, is a double breasted jacket with four buttons on the front that are cut so that the coat buttons on the lower rank below the waist. This gives it a longer line and exposes a little more shirt front so it will wear a bit cooler, which our man on the rail in the illustration must find a blessing as it's apparently so hot that he's had to shed his neck cloth.
Now blazer-appropriate occasions in the dog days of August are blessedly few except by the sea, which is perfect as this style is both nautical and just enough of a dandy's choice to be out of place in church. I doubt if it can be found off the rack and a man who had it made would probably agree that an open weave cloth in marine blue would be best. It should have patch pockets of course, and as little lining as the tailor responsible for it will tolerate.
Wear it with an open collared shirt if there's no other choice but it will look better with a tee shirt in either white cotton or silver silk. A neck cloth is optional.