Hadith no. 1560 (below) is a repeat. Read it here.
Narrated Ibn 'Abbas (radiallaahu `anhu):
A man was crushed to death by his she-camel and was brought to Allah's Apostle (sallallaahu `alayhi wasallam) who said, "Give him a bath and shroud him, but do not cover his head, and do not bring any perfume near to him, as he will be resurrected reciting Talbiya."
Narrated 'Abdullah bin Hunain:
Abdullah bin Al-Abbas (radiallaahu `anhu) and Al-Miswar bin Makhrama (radiallaahu `anhu) differed at Al-Abwa'; Ibn 'Abbas (radiallaahu `anhu) said that a Muhrim could wash his head; while Al-Miswar (radiallaahu `anhu) maintained that he should not do so. 'Abdullah bin 'Abbas (radiallaahu `anhu) sent me to Abu Aiyub Al-Ansari (radiallaahu `anhu) and I found him bathing between the two wooden posts (of the well) and was screened with a sheet of cloth. I greeted him and he asked who I was. I replied, "I am 'Abdullah bin Hunain and I have been sent to you by Ibn 'Abbas (radiallaahu `anhu) to ask you how Allah's Apostle (sallallaahu `alayhi wasallam) used to wash his head while in the state of lhram." Abu Aiyub Al-Ansari (radiallaahu `anhu) caught hold of the sheet of cloth and lowered it till his head appeared before me, and then told somebody to pour water on his head. He poured water on his head, and he (Abu Aiyub) rubbed his head with his hands by bringing them from back to front and from front to back and said, "I saw the Prophet (sallallaahu `alayhi wasallam) doing like this."
Hence proven, that a Muhrim may take a shower and wash his hair as well.
It is permissible for the Muslim to wash his entire body in order to cool down if it is hot. This will give him more energy in order to perform this act of worship. He should take care when washing so that nothing falls from his hair or skin.
Standing Committee for Academic Research and Issuing Fatwas, Fataawa al-Lajnah, 11/184P.S. it's interesting to know the way Prophet (sallallaahu `alayhi wasallam) used to wash his hair - moving his hands front to back and then back to front. Unknown Sunnah, eh?