In the first place, it is to be noted that a man performing Hajj or `Umrah is not permitted to cover his head. This is valid for men because women are required to put on their usual hijab (but not to cover their faces) while performing Hajj or `Umrah. When it is too hot, a pilgrim can use an umbrella.

Tackling this issue in detail, we cite the following fatwa issued by Al-Azhar House of Fatwa:

Covering the head is a restricted action for a pilgrim in Hajj and `Umrah. This means that it is prohibited during ihram. So, if a male pilgrim covers his head in Hajj or `Umrah with something directly touching his head, such as a turban or the like, then he has to make fidyah (expiation). Allah Almighty says: (And shave not your heads until the gifts have reached their destination. And whoever among you is sick or hath an ailment of the head must pay a ransom of fasting or almsgiving or offering.) (Al-Baqarah 2:196)

This verse stipulates the status of those who shave while in ihram. Nevertheless, the Muslim jurists apply it to those who cover their heads, clip their nails, use perfumes, or wear sewn clothes during ihram. They agree that expiation is obligatory in these cases.

So, expiation is obligatory upon undertaking any of the restrictions of ihram. Expiation here is of three kinds, and the person on whom expiation is due has three options: slaughtering a sheep, fasting for three days, or feeding six needy people. He should provide a 1/2 saa` of grain, 1 saa` of dried dates or barley or raisins for each needy person, bearing in mind that one saa` equals about 2.25 kg. This is according to Abu Hanifah’s opinion, which we prefer in this concern. In addition, a man in this situation may give the value of what is mentioned above and distribute it among the poor in the Sacred Precinct if this is easier for him.

On the other hand, there is nothing wrong or haram (forbidden) if a pilgrim takes shelter under an umbrella or a piece of cloth [raised as a canopy or tent]. Umm Husain narrated: “I performed the Farewell Hajj with the Prophet (peace and blessings be upon him). There, I saw Bilal and Usamah. One of them was holding the reins of his camel and the other was sheltering him from the sun with his dress, until he threw the pebbles at Al-`Aqabah.” (Muslim, Abu Dawud and An-Nasa’i)

Therefore, a pilgrim can take shelter from the heat of the sun with an umbrella or a piece of cloth or anything that shelters him without directly touching his head. If he needs to wear a hat or a turban, then he should choose one of the three kinds of ransom mentioned above in the fatwa: either to slaughter a sheep, fast for three days, or feed six needy people with the portion specified earlier. Allah Almighty has prescribed different options for the expiation in order to facilitate things for His servants. Having many options, a Muslim can choose one of them according to his capacity. If a man could not make ransom before he died, then his fate is up to Allah.

Allah Almighty knows best.