Map from Google - Cayo_Largo

In Cayo Largo del Sur, an island located south of Cuba, and famous for its beaches, the climate is tropical, with a relatively cool winter from late November to February, and a hot, muggy and rainy season from May to October. The average temperature goes from 22.5 °C (72.5 °F) in January and February, to 28.5 °C (83.5 °F) in July and August.
Here are the average temperatures.
Average temperatures - Cayo Largo
Cayo LargoJanFebMarAprMayJunJulAugSepOctNovDec
Cayo LargoJFMAMJJASOND
Min (°C)202021222425262625242321
Max (°C)252527282930313130292725
Min (°F)686870727577797977757370
Max (°F)777781828486888886848177

Precipitation amounts to about 1,200 millimetres (47 inches) per year; during the rainy season, from May to October, there is a relative decrease in rainfall in July. The rainiest months are June and September. The summer rains occur in the form of downpour or thunderstorm, which do not decrease the sunshine duration by much. Here is the average precipitation.
Average precipitation - Cayo Largo
Cayo LargoJanFebMarAprMayJunJulAugSepOctNovDecYear
Cayo LargoJFMAMJJASONDY
Prec. (mm)3540404514519512516520012555201190
Prec. (in)1.41.61.61.85.77.74.96.57.94.92.20.846.9
Days665510141113141497114

During the dry season, from November to April, precipitation is not abundant, although some rainfalls may occur, caused by cold fronts coming down from the United States. These cold fronts can lower the temperature by a few degrees, but not at the level of the north side of Cuba. However, from December to mid-March some days can be a bit cool, with highs around 22 °C (72 °F) and lows around 16 °C (61 °F).
On the contrary, from May to October it's hot and humid, though fortunately sea breezes blow.

The amount of sunshine in Cayo Largo is good all year round, however, it's slightly lower from November to February, because of the passage of the aforementioned northern fronts.

In the period from June to November, Cayo Largo like the rest of the Caribbean, can be affected by tropical storms and hurricanes, which however are more likely between August and October.

Cayo Largo

For swimming, the sea is warm all year round, as you can see in the following table.
Sea temperature - Cayo Largo
Cayo LargoJanFebMarAprMayJunJulAugSepOctNovDec
Cayo LargoJFMAMJJASOND
Sea (°C)272626272829293030292827
Sea (°F)817979818284848686848281

When to go

The best time to go to Cayo Largo, for swimming and sunbathing, runs from December to April. In May, you can still go, because the hurricane season has not yet started, although the heat begins to be felt and thunderstorms begin to be quite frequent. From December to mid-March, it may be useful to bring a sweatshirt for cool evenings. All in all, the best time goes from mid-March to late April.