Map from Google - Jamaica

In Jamaica the climate is tropical, hot all year round, with little difference between winter and summer (just a few degrees). Even in winter, the maximum temperatures are around 27/30 °C (81/86 °F), and minimum temperatures around 20/23 °C (68/73 °F). The southern coast, where the capital Kingston is located, is slightly warmer in the winter months, so that the maximum temperature is around 30 °C (86 °F) even in January.
Here are the average temperatures of Kingston.
Average temperatures - Kingston
KingstonJanFebMarAprMayJunJulAugSepOctNovDec
KingstonJFMAMJJASOND
Min (°C)212122232424242424232322
Max (°C)303031313232333332323131
Min (°F)707072737575757575737372
Max (°F)868688889090919190908888

The main difference between the seasons is found in rainfall and air humidity: the rainy season, from late April to October, is hot and muggy. Rainfall occurs mainly in the form of thunderstorm in the late afternoon. In almost all of Jamaica, except in the west coast (see Negril), in July there is a relative lull in precipitation, and in any case there are two peaks in May and October, that is, at the beginning and the end of the period.
The rain pattern is also related to the north-east trade winds, which are typical of the Tropics, and blow from November to March. Along the northern coast of Jamaica, rainfall ranges between 1,200 and 1,800 millimetres (47 and 70 inches) per year. The southern coasts and plains are less rainy than the northern slopes, because they are sheltered from the trade winds by either the Blue Mountains or the hills of the west-central part of the country: these elevations receive a lot of rainfall and are covered by forests (especially the Blue Mountains and the southern part of the Trelawny Parish). Therefore, the capital Kingston is not very rainy, in fact here about 800 mm (31.5 in) of rain per year fall; even the Pedro Plains in the west receive little rain, around 800 millimetres (31.5 inches) per year.
Here is the average precipitation in Kingston.
Average precipitation - Kingston
KingstonJanFebMarAprMayJunJulAugSepOctNovDecYear
KingstonJFMAMJJASONDY
Prec. (mm)2020204010075401001151756545815
Prec.(in)0.80.80.81.63.931.63.94.56.92.61.832.1
Days55578769111410693

The amount of sunshine in Kingston is good even during the rainy season (when there are still 8 hours of sunshine per day).
Quite different is the rainfall in the north coast, exposed to the northeast trade wind, as you can see from the average precipitation of Ocho Rios. Here there is even a peak in the first months in which the trade winds blow, that is in November and December, when the sea retains the heat of summer.
Average precipitation - Ocho Rios
Ocho RiosJanFebMarAprMayJunJulAugSepOctNovDecYear
Ocho RiosJFMAMJJASONDY
Prec. (mm)15012075110165110801001201902502051675
Prec.(in)5.94.734.36.54.33.13.94.77.59.88.165.9
Days7667121213131416108124

From December to March, sometimes the island is hit by the Norte, a cool wind from the United States, which however at this latitude does not lower the temperature too much, in fact it can bring at most a little cool in the evening and at night.
Like the rest of the Caribbean, in the period from June to November Jamaica can be affected by hurricanes, which, however, are more likely between August and October.

Jamaica

For swimming, the sea is warm enough all year round, ranging from 27 °C (81 °F) from January to April, to 29 °C (84 °F) from July to November.
Sea temperature - Jamaica
JamaicaJanFebMarAprMayJunJulAugSepOctNovDec
JamaicaJFMAMJJASOND
Sea (°C)272727272828282929292828
Sea (°F)818181818282828484848282

When to go

The best time to visit Jamaica as a whole, whether you intend to visit cities and make excursions, or to swim and sunbathe, runs from January to April. Indeed, it is the period when the rains are more scarce, and the air is less hot. The absolute least rainy months are February and March, while December is still quite rainy in the easternmost region and in the northern slopes of the Blue Mountains (otherwise, in the south, even December would be fine).
In summer, and generally during the rainy season, the heat is sweltering and annoying; however in Kingston and on the southern coast, in July it usually does not rain much, so if you want to choose the summer, you can choose this month. From June to November, however, you must take into account the risk of hurricanes, which are most likely between August and October.

What to pack

From November to April: light clothes, a sweatshirt for the evening; for the mountains, jacket and hiking boots.
From May to October, tropics-friendly, lightweight clothing, possibly a light sweatshirt and a light raincoat for thunderstorms; a sweatshirt or sweater for the mountains.