According to Shia Islam there is no proved evidence that show prophet himself did Mutah.
But please note when permission of an action is proved by Quran or authentic hadith there is no need for evidence that prophet or Ahl ul-Bayt practiced it and the evidence from Quran or Haith is enough to it be considered permitted.
There is a verse in Quran and many hadith in Shia Hadith books and some hadith in sunni Hadith books proving prophet permitted Mutah to sahaba and sahaba practiced Mutah. so there is enough proof for considering Mutah Halal even if no evidence is found prophet himself did or not.
Temporary Marriage in Islamic Law
http://islamquest.net/fa/archive/question/4634 (you can use google translate to read.)
http://islamquest.net/fa/archive/question/915 (containing many evidence from sunni books)