Map from Google - Djibouti

The climate of Djibouti is tropical desert in the coast and in the north, while it becomes semi-desert in south-central highlands.
Along the coast, where the capital Djibouti is located, it's hot all year round.
During winter, from December to February, the temperature is high, around 84 °F during the day. The amount of sunshine is high, the rains are rare, and the air is moist, but the cool sea breeze blows.
Starting from March, the temperature gradually increases, and the heat becomes intense, especially in May when the daytime temperature fluctuates around 95 °F, with warm nights, and still with damp air.
In June, the summer begins, characterized by an intense but drier heat, especially in June and July, when a wind from the desert, called Khamsin blows, which can lift dust and sand and reduce visibility. Summer continues until September with really high temperatures, often exceeding 105 °F, while at night the temperatures stay around 85 °F. On the coast, in the afternoon the sea breeze can lower the temperature, while increasing moisture. September is perhaps the worst month, as temperatures remain high but the atmosphere returns to be quiet and the humidity from the sea makes the heat oppressive. In October, the heat continues to be sultry, but the temperatures decrease a bit and become similar to those of May.
Here are the average temperatures of Djibouti City.
Average temperatures - Djibouti
Min (°F)727375778184888884797372
Max (°F)848486909510210810699918884

In Djibouti City, about 4.8 inches of rain per year fall: this value is typical of a desert climate. Here is the average precipitation.
Average precipitation - Djibouti
Prec. (in)

In the inland region, the climate becomes semi-desert in the south-central highlands, for instance in the Day Forest National Park, where there are hills and canyons reaching up to 5,600 feet, or in southern cities as Randa, Arta, Holl-Holl, while in the north, Mount Moussa Ali, the highest peak of the country with its 6,600 feet, is desert. In fact, the central and southern inland areas can get some rain in the period from July to October, being touched by the summer monsoon, and also some additional rain during winter, from November to March. Showers are rare, but sometimes intense, so that occasionally the wadis, the riverbeds which remain dry for most of the year, can be turned into streams and may overflow creating landslides and floods, as occurred in November 1994, April 2004 and March 2013. In the central and southern highlands, the annual rainfall ranges from 8 and 12 inches.
Here is the average precipitation in Ali Sabieh, located in the south, at 2,300 feet above sea level.
Average precipitation - Ali Sabieh
Ali SabiehJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (in)

The temperature decreases with altitude, but remains high even at this altitude of 2,300 feet. Here are the average temperatures.
Average temperatures - Ali Sabieh
Ali SabiehJanFebMarAprMayJunJulAugSepOctNovDec
Min (°F)636668727377797775706663
Max (°F)818286889197999988888482

In Djibouti there is also a depression, where the salt lake Assal is located, at 490 feet below sea level. In the west, there is a larger saltwater lake, Lake Abbe.

Lake Assal

The sea is warm throughout the year, and in summer it becomes very warm: the temperature goes from 79/81 °F in winter, to 84/88 °F in summer.
Sea temperature - Djibouti
Sea (°F)797981828688868486868281

When to go

The best time to travel to Djibouti runs from December to February, being the least hot of the year. Even November and March are generally acceptable months, although a bit warmer, around 86/90 °F during the day. The worst time is the long summer, due to the scorching heat.
During the summer, the sea is so warm as to allow long dives in the reef, and bathing is also a way to escape the oppressive heat.

What to pack

In winter: on the coast, summer clothes, possibly a light sweatshirt for the evening; for the reef, equipment for snorkeling, water shoes or rubber soled shoes. In inland areas, light clothes, sun hat, desert turban, hiking shoes, sunscreen, sweatshirt for the evening. In the mountains, sweatshirt and light jacket for the evening.

In summer: on the coast, tropics-friendly, lightweight clothes; for the reef, equipment for snorkeling, water shoes or rubber soled shoes. In inland areas, lightweight clothes, of natural fabric (cotton or linen), desert turban; possibly a light raincoat for the rain showers. For women, it is best to avoid shorts and miniskirts. In the mountains, a sweatshirt for the evening.