Zaid Alsalami, Shaykh Dr Zaid Alsalami is an Iraqi born scholar, raised in Australia. He obtained a BA from Al-Mustafa University, Qom, and an MA from the Islamic College in London. He also obtained a PhD from... Answered 5 months ago

Bismihi ta'ala
 

Temporary marriage can only be performed with a woman who is from Ahlul Kitab, i.e. she is either a Muslim, a Christian or a Jew. 

If she is of any other faith, or just believes in a supreme being, but does not follow any of the 3 Abrahamic religions, then you cannot do mut'ah with her.

And Allah knows best.