Almighty Allah says, (And He has not laid upon you any hardship in religion) (Al-Hajj 22:78). This divine declaration is a general principle according to which various sorts of rukhsahs (concessions) have been established by Muslim jurists. No Muslim should suffer any difficulty due to his or her religious obligations.

Responding to this question, the Standing Committee for Islamic Research and Ifta’ stated,

If the situation is as described, then the Hajj will be valid. It is not a sin to wear clothes other than the ihram garment to ward off any hardship.

But he has to offer a fidyah (expiation) for that, which is to feed six of the poor people of the Haram (sanctuary), or to slaughter a sheep that is fit to be offered as a sacrifice and feed the poor people of Makkah or the rest of the sanctuary with its meat. But you should not eat any of it. You may also fast for three days. Whichever he does will be acceptable. The pilgrim would also have to do the same thing if he covers his head.