Noun. A girlfriend who for either personal, religious or other reasons, will not have sex with you, but continues to go out on dates. As in "at a temp agency, you have a job, just no benefits. Temp agency girlfriend you have a girlfriend, just no benefits."
John- "hey man, you still dating Nikki-no-sex?"
Mike- "no, I dumped her over email."
John- "yeah, about time you dumped your temp agency girlfriend."