Questions and Answers

One of our scholars, Yahya bin al-Hussein al-Hūthi responded to this question. Below is a synopsis of his reply in his book Al-Jawâb ar-Râqi [I have edited it for length]:

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Another difference between us and them is temporary marriage. We prohibit it based on the narration of Imam Zayd bin ‘Ali on the authority of his father--‘Ali, upon him be peace, who said: "The Messenger of Allah, peace and blessings be upon him and his progeny, forbade temporary marriage in Khaybar."

The proof for its abrogation and proscription is a narration in the Amâli of Ahmed bin ‘Isa bin Zayd bin ‘Ali that was narrated by Muhammad bin Mansūr al-Murâdi, may Allah’s mercy be upon him. He said: Muhammad—Ahmed bin ‘Isa bin Zayd—Hussein bin Alwân—his father, Khâlid—Zayd bin ‘Ali—his father—‘Ali, upon him be peace, said: “The Messenger of Allah, peace and blessings be upon him and his progeny, prohibited temporary marriage for us during the battle of Khaybar.” 
Mu`ayyad Billah, upon him be peace, relates in his chain of authorities on the authority of ‘Abdullah—Hassan—his father—his grandfather—‘Ali, upon him be peace, said: “The Messenger of Allah prohibited temporary marriage of women during Khaybar. He said: ((One does not perform this action except that he is flogged.))” 
In the Amâli narrated by Muhammad—al-Qâsim bin Ibrâhîm—Ismâ’îl bin Abi Uwais—Hussein bin ‘Abdullah bin Ďamīra—his father—his grandfather—‘Ali said: “The Messenger of Allah, peace and blessings be upon him and his progeny, prohibited temporary marriage.” 
Concerning its prohibition, ‘Abdullah bin Hassan narrates that it was held by the Ahl al-Bayt; his son, Muhammad bin ‘Abdullah Nafs az-Zakiyya, Zayd bin ‘Ali, Ja’far as-Sâdiq, Qâsim bin Ibrâhîm, and Ahmed bin ‘Isa.