Jacques Herzog, Hon. FAIA, has mixed feelings about Miami. On the one hand, he says, “In Miami, more than in any other American city, you have everything”: the weather, the food, the cultural pulse of the city’s immigrant communities, all hold a potent appeal for the acclaimed Swiss designer. On the other hand, Herzog has harsh words for the city’s signature architectural style—“Art Deco is the wrong approach”—and for the many of its confined, over-air-conditioned spaces—“Women, they have to go around wearing fur coats.”

The latest project from Herzog and partner Pierre De Meuron, Hon. FAIA, is intended as an antidote, a building that will reconnect Miamians to their superb natural climate while abjuring the highly stylized architectural gestures that have prevailed here since the days of Deco. With the annual Art Basel Miami festival carrying on at full blast from North Beach to the Design District, Herzog was in town to check on the progress of the still-under-construction Miami Art Museum (expected to open in late 2013), the new home of the city’s nearly 30-year-old treasure house of paintings and sculpture.

The design, especially as seen from the exterior, is something new for Herzog & de Meuron, a temple-like box reminiscent of the grand culture palaces of old, with a colonnade of slender concrete piers along the eastern façade. The reference is deliberate, Herzog says. He places its “classical” profile in a continuum with the stone-built temples of antiquity, based on a still older tradition of rustic wooden building: “What we do here is like a petrified wood construction, like Japanese architecture or Greek temples,” he says.

Where the structure breaks free of the box, and of history, is in its openness. Long sight lines afford views from the interior to the surrounding park and waterfront, making nearly every gallery feel a part of the landscape. The effect is achieved through the informal disposition of is the exhibition rooms, and it creates what museum director Thom Collins calls a “polyvocal” effect—rather than proceeding along a predetermined route, visitors create their own narrative as they move freely through the museum.

But the building’s most unique feature (also its most typically Herzog & de Meuron-esque) is the enormous volume of vegetation that will cling, hang, and grow on all four sides, with trees poking up through the interstices of the structure and creeping vines adhering to the vertical supports. The plant life wasn’t in place yet; but when it is, it promises to give locals a shady outdoor space that will get them out of the stylish glass towers of downtown and back onto the shores of Biscayne Bay.