Bedouins wear black robes, the guardian did some tests and they found out the amount of heat the wearer is exposed too is the same with black and white robes.

Taylor, Finch, Shkolnik, and Borut measured the overall heat gain and loss suffered by a brave volunteer. They described the volunteer as “a man standing facing the sun in the desert at midday while he wore: 1) a black Bedouin robe; 2) a similar robe that was white; 3) a tan army uniform; and 4) shorts (that is, he was semi‑nude)”.

Each of the test sessions (black-robed, white-robed, uniformed and half-naked) lasted 30 minutes. They took place in the Negev desert at the bottom of the rift valley between the Dead Sea and the Gulf of Eilat. The volunteer stood in temperatures that ranged from a just-semi-sultry 35C (95F) to a character-building 46C (115F). Though he is now nameless, this was his day in the sun.

The results were clear. As the report puts it: “The amount of heat gained by a Bedouin exposed to the hot desert is the same whether he wears a black or a white robe. The additional heat absorbed by the black robe was lost before it reached the skin.”

Bedouins’ robes, the scientists noted, are worn loose. Inside, the cooling happens by convection – either through a bellows action, as the robes flow in the wind, or by a chimney sort of effect, as air rises between robe and skin. Thus it was conclusively demonstrated that, at least for Bedouin robes, black is as cool as any other colour.

Source

Depending on of the fabric and how tight it is to the body black can keep you as cool.