Mutah is a type of marriage in which period of marriage is already decided when it takes place. In short Nikah E Mutah means temporary marriage. According to Sunni Islam Mutah is haram In Islam because Prophet Muhammad Peace be upon him prohibited from it on the day of Khyber and declared it haram till Judgement day. On day hand Shia scholars says Mutah is Halal.
When we see books of hadiths we find many narrations on this Issue. According to Sahih Bukhari Volume no 5, Book no 59, hadith Number 527:
On the day of Khyber, Allah's Apostle forbade the Mut'a (i.e. temporary marriage) and the eating of donkey-meat.If we see Sahih Muslim Book no 008, hadith Number 3259:
Rabi' b. Sabra reported on the authority of his father that Allah's Apostle (may peace be upon him) prohibited the contracting of temporary marriage.Now lets see what some of authentic Shia Books says about Mutah:
Imam Ali (A.s) states that the Prophet made Mut'ah haram on the day of Khayber.
Tahdeeb: vol. 7, pg. 251, rewaya 10
Aba Abdullah (as) said about Mutah: 'Abandon it, aren't anyone of you ashamed of exposing his private parts.
Wasael Alshia Pp22.V21/ Pp44.V2
Ja'far Al-Sadiq says "I asked Abu Abdullah (as) about Mutah. He said: "Don't defile yourself with it".
Bihaar Al-Anwar, Volume 100, page 318
Narrated from Imam Jaffar Ul Sadaq (A.S) Mutah is Adultery.
Kitab ul Mola. Pp412.V21there are plenty of more references from shia books which clearly says that Mutah is haram and was forbidden by Rasool Allah S.A.W on the day of Khyber. So if you are true follower of Prophet S.A.W follow his orders.