When you have a particularly troubling problem regarding Islamic doctrine, don’t waste time. Go straight to the man himself, the Grand Ayatollay Sistani! He answers questions personally on his web site.

One feature of the Islamic faith that’s particularly interesting is the establishment of Temporary Marriage. Marriage is often temporary in western culture, but it generally isn’t planned that way.

Question : I want to do Muta’h marriage, what are the rules?

§ Answer : Temporary marriage has the following rules:
If you have already a Muslim wife, you can marry another Muslim woman. You cannot have Muta’h contract with a woman from ahle-kitab (People of the Book) unless your Muslim wife agrees with it. If she disagrees, it is haram (illegal). Temporary marriage with a kafir (an unbeliever who does not belong to Ahle Kitab) is absolutely forbidden.
However, in temporary marriage, you will have to read Sigha and you should follow the rules of a permanent marriage. In the Sigha, you will mention time (duration) and Mahr (dowry). Without specifying them marriage would be void. Moreover, it is necessary to read the sigha either yourself or make someone else your wakil (representative) to read it on your behalf.
This is how the Sigha (Verbal Contract) should be read by both sides:
First the wife says: MATTA’TUKA NAFSI FIL MUDDATIL MA’LUMA ‘ALA AL-MAHRIL MA’LOOM.
Then the man says: QABILTU

Or he can say: ATAZAWWAJOKA FIL AL-MUDDATIL MALOOMA ALA AL-MAHRIL MA’LOOM
The woman says: Qabiltu

Everything is translated well, but the Scientific Genius part of the site is pretty confusing. There was a disappointing lack of hard science to back up the claim of genius.