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 29 °C (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 35 °C (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 often blows, which can lift dust and sand and reduce visibility. Summer continues until September with really high temperatures, often exceeding 40 °C (104 °F), while at night the temperatures remain around 30 °C (86 °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
DjiboutiJanFebMarAprMayJunJulAugSepOctNovDec
DjiboutiJFMAMJJASOND
Min (°C)222324252729313129262322
Max (°C)292930323539424137333129
Min (°F)727375778184888884797372
Max (°F)848486909510210810699918884

In Djibouti City, about 120 millimetres (4.7 inches) of rain per year fall: this value is typical of a desert climate. Here is the average precipitation.
Average precipitation - Djibouti
DjiboutiJanFebMarAprMayJunJulAugSepOctNovDecYear
DjiboutiJFMAMJJASONDY
Prec. (mm)105101891011125101110121
Prec.(in)0.40.20.40.70.40.40.40.50.20.40.40.44.8
Days00123334311122

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 as high as 1,700 metres (5,600 feet), or in southern cities such as Randa, Arta, Holl-Holl, while in the north, Mount Moussa Ali, the highest peak of the country with its 2,000 metres (6,500 feet), is desert. In fact, the central and southern inland areas can receive some rain in the period from July to October, being affected by the monsoon of the Arabian Sea, and also some additional rain in winter, from November to March. Showers are rare, but sometimes intense, so that the wadis, the riverbeds that remain dry for most of the year, can occasionally turn 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, annual rainfall ranges from 200 to 300 millimetres (8 to 12 inches).
Here is the average precipitation in Ali Sabieh, located in the south, at 700 metres (2,300 feet) above sea level.
Average precipitation - Ali Sabieh
Ali SabiehJanFebMarAprMayJunJulAugSepOctNovDecYear
Ali SabiehJFMAMJJASONDY
Prec. (mm)10153550301050704010105335
Prec.(in)0.40.61.421.20.422.81.60.40.40.213.2
Days12234434421131

The temperature decreases with altitude, though it remains pretty high even at 700 metres (2,300 feet). Here are the average temperatures in in Ali Sabieh.
Average temperatures - Ali Sabieh
Ali SabiehJanFebMarAprMayJunJulAugSepOctNovDec
Ali SabiehJFMAMJJASOND
Min (°C)171920222325262524211917
Max (°C)272830313336373731312928
Min (°F)636668727377797775706663
Max (°F)818286889197999988888482

In Djibouti there is also a depression, where the salt lake Assal is found, at 150 metres (490 ft) below sea level. In the west, there is a larger saltwater lake, Lake Abbe.

Lake Assal

The sea in Djibouti is warm throughout the year, and in summer it becomes very warm: the water temperature goes from 26/27 °C (79/81 °F) in winter, to 29/31 °C (84/88 °F) in summer.
Sea temperature - Djibouti
DjiboutiJanFebMarAprMayJunJulAugSepOctNovDec
DjiboutiJFMAMJJASOND
Sea (°C)262627283031302930302827
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. November and March are generally acceptable months as well, although a bit hotter. 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. For women, it is best to avoid shorts and miniskirts.

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. In the mountains, a sweatshirt for the evening. For women, it is best to avoid shorts and miniskirts.