Map from Google - Turks_and_Caicos

The Turks and Caicos Islands have a tropical climate, hot all year round, with a hotter and muggy season from May to October, and a relatively cool season from December to March.
The temperatures are high throughout the year: the daily average is around 23.5 degrees Celsius (74.5 °F) in winter, and 28 °C (82 °F) in summer. From December to March, sometimes the cool wind from the United States can lower the temperature by a few degrees, so that the minimum can drop below 20 °C (68 °F). Summer is sultry, but the heat is tempered by the breeze.
Here are the average temperatures of Cockburn Town, in the island of Grand Turk.
Average temperatures - Grand Turk
Grand TurkJanFebMarAprMayJunJulAugSepOctNovDec
Grand TurkJFMAMJJASOND
Min (°C)202020212223242423232221
Max (°C)272728293031323232312927
Min (°F)686868707273757573737270
Max (°F)818182848688909090888481

As regards the rains, the archipelago is a bit arid as compared with other Caribbean islands: rainfall amounts to around 700/750 millimetres (27/29 inches) per year, and the rainy season, which in the rest of the Caribbean usually sees heavy rainfall from May and October, here is shorter and moved forward, between September and December, and it is not particularly intense: the rainiest month is November with 120 mm (4.7 in).
Here is the average precipitation.
Average precipitation - Grand Turk
Grand TurkJanFebMarAprMayJunJulAugSepOctNovDecYear
Grand TurkJFMAMJJASONDY
Prec. (mm)55453545454035457090120100725
Prec.(in)2.21.81.41.81.81.61.41.82.83.54.73.928.5
Days8678111111121314108119

However, throughout the year and especially in summer, short rain showers can occur, which quickly give way to the sun. In fact, the amount of sunshine is good all year round, as you can see in the following table.
Sunshine - Grand Turk
Grand TurkJanFebMarAprMayJunJulAugSepOctNovDec
Grand TurkJFMAMJJASOND
Sun (hours)777877887766

In the period from June to November, tropical depressions and hurricanes can hit the Turks and Caicos Islands, as is typically the case in the Caribbean. However, hurricanes are more likely in the period from August to October.

Turks and Caicos

For swimming, the sea is warm enough all year round, as we can see in the following table.
Sea temperature - Grand Turk
Grand TurkJanFebMarAprMayJunJulAugSepOctNovDec
Grand TurkJFMAMJJASOND
Sea (°C)262626262728282929292827
Sea (°F)797979798182828484848281

When to go

If it were not for the risk of hurricanes, the Turks and Caicos could be visited at any time of the year. The period from May to October is the most hot and humid, while the period from September to December is quite rainy, even though the rains occur mostly in the form of downpour or thunderstorm in the afternoon or evening, and do not last long. From December to March, some days can be a bit cool and breezy, but usually not to the point of disturbing those who are on the beach. So the best time is from January to April, and April is probably the best month overall.

What to pack

From December to April: light clothes, a sweatshirt for the evening.
From May to November: tropics-friendly, light clothing, possibly a light sweatshirt and a light raincoat for thunderstorms.