Map from Google - Fernando_de_Noronha

The climate of the archipelago of Fernando de Noronha, near the northeast coast of Brazil, is tropical, hot all year round, with a dry season from August to January, and a rainy season from February to July. The archipelago is a UNESCO World Heritage Site.
Given the proximity to the Equator, the temperatures are stable throughout the year, and are slightly higher from November to April, when highs are around 86 °F, and slightly lower from May to October, when they are around 82/84 °F. At night, the temperature almost never drops below 68 °F.
Here are the average temperatures.
Average temperatures - Fernando de N.
Fernando de N.JanFebMarAprMayJunJulAugSepOctNovDec
Min (°F)777777757575757575757777
Max (°F)868686868484828284848686

In a typical year, about 56 inches of rain fall; the wettest months are March, April, May and June, when the rains are equal to or exceed 8 inches per month. Generally, the rainfall amount in February and July is acceptable, but in some years it may be more abundant, reaching the level of the rainiest months.
Here is the average precipitation.
Average precipitation - Fernando de N.
Fernando de N.JanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (in)2.64.310.411.4117.

The driest period, in which it rarely rains, runs from September to December. October is historically the driest month, with fewer deviations from the norm, while in the other dry months, every once in awhile an intense shower may occur.
The rainfall distribution in Fernando de Noronha is similar to that of cities located in the north-east of Brazil, like Fortaleza and Natal.
Air humidity is high throughout the year, even in the dry season; however, fortunately sea breezes give a bit of relief.
The amount of sunshine is never scarce, because the rains come in the form of downpour or thunderstorm, and usually do not last long, however, the sunniest period is the dry season.

Sea in Fernando de Noronha

For swimming, the sea is warm all year round, as you can see in the following table.
Sea temperature - Fernando de N.
Fernando de N.JanFebMarAprMayJunJulAugSepOctNovDec
Sea (°F)828282848282818181818181

When to go

The best time to visit the archipelago of Fernando de Noronha, to explore the islands on foot, or for sunbathing, swimming and diving, goes from August to January, being the driest of the year. Surfers will appreciate especially the period beginning in November and peaking in February and March, when waves are higher.