It’s not an oxymoron. Rather, it is more a state-of-mind. That same state-of-mind that has you wearing custom clothing to begin with.
So, consider a pair of linen blend trousers this summer. Sure they wrinkle, so do cotton. But they’ll keep you cooler and look better with a few wrinkles anyway. Wear them flat-fronted, or trim-cut and pleated.
Try a sportcoat in a linen and silk blend. With minimal lining and patch pockets, it is guaranteed to beat the heat. Those great colors are nothing to shy away from. Stronger sunlight calls for a more vibrant color to stand up to it.
For the truly inspired, a linen suit (younger guys wear this with a v-neck t and sandals). I’m particularly fond of the navy windowpane on the right panel, above. And it looks equally good with an open collar shirt or a golf shirt under it.