Here is a rational discussion on the apparent disagreement between the sages:
http://www.askmoses.com/en/article/247,2100722/Who-Will-Build-the-3rd-Temple.html#articlepageWe can now approach the primary question about the Third Temple. How will it be built? This is an issue that few people are willing to address because of obvious political implications. But, like it or not, the Third Temple is going to be built one day. So we may as well look at the question now.
There is an essential disagreement among authorities as to how the Third Temple will be built. According to the Rambam (Maimonides), in his work, the Jewish people are commanded to construct a House for G-d.1 The Rambam lists this as one of the 613 eternal commandments of the Torah, relevant and obligatory whenever the Temple is not standing. He derives this from the verse, "And they shall make for Me a sanctuary, and I will dwell among them."2 According to the Rambam, the Jewish people must build the Third Temple any way they can, at any time they can accomplish the task. In the Laws of Kings, the Rambam states that the Messiah, an earthly, Jewish king, will build the Third Temple. And, in fact, he states that the only conclusive proof of the identity of the Messiah is that he will be the one to build the Temple.3
The other view on the subject is derived from Medrash Rabbah, (a book of homiletic expositions from the time of the Talmud) . Here, the Medrash teaches that G-d Himself will build the Third Temple, and it will descend out of the fire from Heaven, onto its appointed place on earth, the Temple Mount. Rashi (the chief and classical bible commentator, circa 1200 C.E.) and Tosefot, (an academy of European scholars circa 1300C.E.) and many other authorities subscribe to this view, and this has become the popular view of the Jewish people. As to the verse, "They shall make for Me a Sanctuary," this opposing view teaches that the directive was already fulfilled with the building of the Mishkan and the first two Temples, and is no longer applicable. They cite as the source for the Third Temple the verse, "You shall bring them in and plant them in the mountain of Your inheritance, in the establishment of Your residence which You have made, O Eternal, the Sanctuary, G-d, which Your hands have established."4
Although the two views appear to be contradictory, both are the words of the Living G-d, and there is no contradiction here at all. Among the many explanations which resolve the argument is the teaching that the redemption (and therefore the Third Temple) can come in one of two ways, b'itoh (in its time) or achishenah (suddenly, at any moment). B'itoh is the end of the fifth milennia, the Jewish year 6000 (as of this writing we are in the year 5759). If final redemption does not come till then, the Jewish people, led by the Messiah, who will be anointed as king by a prophet of G-d, will build the Third Temple. This goes according to the Rambam. But if the redemption comes achishenah, that is, immediately if not sooner, it will be replete with manifold miracles, incomparably greater than during the Exodus from Egypt some 3309 years ago, and the Holy Temple will suddenly appear out of the fire of Heaven atop Mount Moriah in Jerusalem. This is the opinion of Rashi and Tosefot, and the hope and dream and yearning of the Jewish people.
This explains the contradiction, but it does not resolve it. And one does not push away the Rambam with a toothpick. For the Rambam could tell you, "Is that so? Well, the commandments are eternal and G-d has no right to take one of them away from us. So don't give me this 'appearing out of the fire of Heaven' stuff."
The question then becomes, "How can G-d send the Temple down from Heaven already built, yet have it built on earth by the Jewish people?"
In Ohr HaMikdash (Light of the Holy Temple), Rabbi Raphael Moshe Luria resolves the paradox a number of ways. He cites the principle of a hechsher Mitzvah, that is, an act that causes a mitzvah to be fulfilled. For example, the last commandment of the Torah (number 613) commands us to write our own Torah scroll. This is an extraordinary task that few people are capable of performing. It takes years of training to become a scribe, and a trained scribe will spend a year or longer writing a Torah, which must be copied letter by letter from an existing Torah. If one letter is missing or written incorrectly, the Torah is invalid, and considered as no Torah at all.
