That is hard to say. Air is kind of personal.My sister in the States put on the air in the car when it was 68 degrees out.
Our hottest month is May. In June and July it rains a bit in short cool bursts and many folks think it is the nicest time of the year. Sometimes Aug is like July, Sometimes it is like Sept-rainy season.
It also depends where you stay. Diane's Beachouse is cool inside in summer.Some hotels are not always cool.
It is worth noting that millionares who live on Caye Caulker do not have air in their houses, though one or two smaller homes have it.