Non-Muslims are of two types: 1. People of the Book 2. Not People of the Book. According to the view of all Shia jurists, a Muslim man cannot get married (neither temporarily nor permanently) to a non-Muslim woman who is not of the People of the Book.
In this regard, Imam Khumayni says: “… The Muslim man cannot get permanently married to non-Muslim women who aren't of the People of the Book, and as per obligatory precaution, also cannot get permanently married to non-Muslim women who are of the People of the Book.”
Of course, Imam Khumayni (rah) has said in this issue (the issue of permanent marriage with non-Muslim women who are of the People of the Book) that it is an obligatory precaution, which means those who follow him can refer to the verdict of another jurist who says such a marriage is permissible and follow him instead.
Temporary marriage with non-Muslim women who are of the People of the Book is permissible according to the verdict of all contemporary jurists.
As to whether or not it is necessary for a non-Muslim virgin girl who is of the People of the Book to get permission from her father before contracting temporary marriage, it depends on their religion and whether or not the father’s permission is a condition therein. 
 See: Tawdih al-Masa’il (annotated by Imam Khumayni), vol. 2, p. 468, issue 2397.
 Ayatullah Nouri Hamedani: Rather, it is even permissible to get permanently married to them according to the stronger view, nonetheless, such a marriage should be refrained from if one can get married to Muslim. Ayatullahs Golpaygani and Saafi: The validity of getting permanently married to a non-Muslim woman who is of the People of the Book isn't devoid of strength [it is permissible], yet if one can get married to a Muslim woman, then it [marrying a non-Muslim woman who is of the People of the Book] will be very makruh; as a matter of fact, precaution should not be abandoned here. Ayatullah Zanjani: The Muslim man cannot get married to the Magi or a non-Muslim who is not of the People of the Book, neither permanently nor temporarily, and apparently, permanent or temporary marriage with Jewish or Christian women isn't void, but it is makruh and against recommended precaution, especially if the marriage is permanent. See: Tawdih al-Masa’il of the maraji’ (annotated), vol. 3, p. 468.
 Ibid, for information on the verdicts of past jurists, see: Al-Fiqh ala al-Madhaahib al-Khamsah, Muhammad Jawad Mughniyah, vol. 2, pp 47-49.
 Tahrir al-Wasilah, vol. 2, p. 285, issue 2.
 For further information, see: Marrying Christians, Question 826.