Unlined cotton blazers are the secret to dressing dapper in the Summer.
An "unlined" blazer still has shoulder and chest lining/padding, but the rest of the jacket does not. It's a more casual style but you're shedding those thick layers that make a suit in the Summer heat so unbearable. Most linen suits are unlined as well.
Sometimes it's just so incredibly hot on a New York City subway platform that you have to ditch the blazer till you get where you're going. Just wear a polo or elevated knit underneath. A knit can be just as dapper if you style it up the right way. I avoid ties in July and August at all costs!
Take a cue from Pitti Uomo and crop your pants with an extra roll. Italian men do dapper the best. Look to them for your sartorial advice!