Map from Google - Christmas_Island

The climate of Christmas Island, a territory of Australia located in the Indian Ocean, is tropical, with stable temperatures, around 79/81 °F during the day from June to November, and around 82/83 °F from December to May.
Here are the average temperatures of Flying Fish Cove (or The Settlement).
Average temperatures - The Settlement
The SettlementJanFebMarAprMayJunJulAugSepOctNovDec
Min (°F)737373737573737272737373
Max (°F)828282828281797979818182

The main difference in the climate is found in the rainfall, which amounts to 8 inches per year and is much more abundant in the rainy season, from November to June, when the north-western monsoon prevails, while the rains are rarer and shorter from July to October, when the south-east trade winds prevail. The rainiest months are January and February, when about 11.5/13.5 in of rain per month fall, while the driest months are August and September, when precipitation is about 1.7/2 inches per month. Here is the average precipitation.
Average precipitation - The Settlement
The SettlementJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (in)11.613.811.

The north-west monsoon is accompanied by high humidity, which brings low clouds and mists above the inland hills, where a forest grows; it may also be accompanied by strong winds that hit in particular the northern coast, and occasionally by cyclones. The Christmas Island is actually on the edge of the area in which the tropical cyclones of the South Indian Ocean can form (in theory, from November to mid-May, even though in thirty years they have passed over the island only from November to April, with a peak in December), so it is not directly affected by cyclones in the acme of their intensity, but it's touched by tropical storms or by cyclones in the early stages of their formation.
Between October and November, at the beginning of the rainy season, the migration of the island's famous red crabs occurs: millions of crabs come out from the forests, where they had been hiding during the dry season, and migrate to the beach, to mate and lay their eggs.

Red crabs

For swimming, the sea is warm all year round, as you can see in the following table.
Sea temperature - Christmas Island
Christmas IslandJanFebMarAprMayJunJulAugSepOctNovDec
Christmas IslandJFMAMJJASOND
Sea (°F)828484848482818179818282

When to go

The best time to visit the Christmas Island goes from July to October, being the driest and sunniest; in particular the months of August and September are the driest.

What to pack

All year round, light clothes, a scarf for the breeze, a light sweatshirt for the evening, light raincoat or umbrella.