All perfect praise be to Allah, The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
Covering the head, whether by a turban, a hat or any other garment, is forbidden for a man in Ihram (Ritual consecration) since it was narrated from 'Abdullah bin 'Umar that: a man asked the Messenger of Allah what clothes the Muhrim should wear? The Messenger of Allah said: "Do not wear shirts, or 'Imamahs, or pants, or burnouses, or Khuffs except if someone does not have sandals, in which case let him wear Khuffs, and cut them so that they come below the ankles. And do not wear any garment that has been touched by (dyed with) saffron or Wars." {Bukhari}.
However, if a Muhrim used a piece of cloth or an umbrella to protect his head and body from the heat of the sun or from the rain, but without his head being touched or without that item staying on the head directly, then this is permissible, and doesn`t violate the restrictions of Ihram. Al-Imam Ibn Qasim said: "It is forbidden for a man in Ihram to cover his head or part of it by whatever is considered a head cover, such as a turban or mud. But, whatever isn`t considered as such isn`t forbidden." {Shareh Ibn Qasim, 154}. And Allah knows best.