The conditions of temporary marriage :

Is it okay to contract a temporary marriage with a Shia girl without her father’s permission and after having intercourse with her?

According to Islam, fulfilling one’s sexual desires can only be done with the observation of Islamic law. Most of the marja’s today believe that performing the mutah or temporary marriage with a virgin girl can only be contracted with the permission of her father, or her grandfather from the father’s side [when the father isn't alive].
So if a girl comes of age, reaching the age of bulugh and obligation, and is rashidah (meaning that she can tell what is to her benefit and what isn't), she needs to get her father or grandfather’s (in the case of not having a father) permission if she is a virgin. But if she isn't a virgin as a result of legitimate intercourse [with a permanent or temporary husband], there is no longer any need for her father or grandfather’s permission. 
Conclusion: According to most marja’s, any type of marriage must be with the permission of the father or grandfather of the girl and illegitimately losing virginity doesn’t change this ruling whatsoever and their permission remains as one of the conditions of the marriage.