Twenty minutes. A Metromover loop. Free, covered, air-conditioned, elevated one storey above the street with the Brickell leg crossing the Miami River. Ride it as long as you like. This is the cheapest cooling in the city and the only one with a view.
One hour. A single gallery. Wynwood's are free to enter and clustered within a few blocks, and the Design District's contemporary art museum is free permanently, which makes it the best-value cool hour in Miami on any date. A cinema works too, and is unglamorous advice that saves plenty of August afternoons.
Two hours. The downtown art museum, at around $16 for an adult and free to everyone on the second Saturday of the month. Its bayside terrace and hanging gardens are outdoors, so budget the indoor portion honestly.
Three to four hours. The science museum and planetarium next door, around $30, with an aquarium inside it. This is the single strongest indoor block in the city with children, and it is the one to buy for two o'clock rather than eleven, because the morning was always going to be fine outdoors.
A full day. Chain the two downtown institutions with a long lunch between them, or accept a drive to one of the enclosed malls at the county's edges. There is no third answer, and any page that offers you one is padding.
Whatever the length: check the institution's closing day. Several museums here take one early in the week and it varies by place, so confirm the specific one rather than a general list.