Cuba is generally hot all year round. It can be very hot and humid from June to October. The humidity will drop a bit from November and on which will bring in a nicer climate.
May brings the start of the rainy season and the hurricane season which goes through to November. Although it is the rainy season, any rainfall is usually just a 10-20 minute tropical downpour and then back to sunshine and most rain usually occurs in the evenings and throughout the night.