I've read that one of the various reasons that Judaism did not accept Jesus as the prophecies messiah is because the Messiah was supposed to build a third temple. What I'm curious about; the second temple wasn't destroyed until 70AD or so, so in the lifetime of the historical Jesus it was still standing correct? So why was there a prophecy of a third temple needing to be built when there was already a temple standing, and the various Jews living at the time did not know this temple would eventually be destroyed? I'm not a religious person so I doubt any supernatural explanation, I am interested in the historical realities of the period.
There are a number of legal criterion for a prophet in Judaism, none of which were fulfilled by Jesus--most importantly that no true prophet would declare any portion of the law (Torah &Talmud) invalid. From the perspective of the Jewish tradition, any number of statements by Jesus violate this precept--for example, his call for his followers to give up their families and follow him runs directly counter to many of the obligations incumbent upon Jews and contradicts the commandment to honor ones father and mother.
For a more comprehensive but non-academic and accessible take on Jewish responses to Jesus, I'd recommend "A Rabbi Talks to Jesus" by Jacob Neusner.
TL;DR - Rebuilding the temple wasn't the problem with Jesus' 'prophetic' status: there were a whole LOT of other problems from a Jewish perspective, including fundamental differences in ethical approaches and relationship to society.