It may be suggested that the Temple of the future ("it will be revealed and come from heaven already built and perfected") will first be revealed in the place "That the Temple traveled and settled there" in the time of exile ("The House of our Rebbe in Bavel"); from there it will be transported to its place in Yerushalayim.
...Perhaps it can be said that this is alluded to in the Rambam's choice of words (in Hilchos Melech HaMoshiach) "And build the Temple in its place." For apparently [there is a question]: what is the need to inform us here that the building of the Temple will be in its place? On the other hand, why isn't the place specified: "And build the Temple in Yerushalayim?" [It must be] that "in its place" alludes as well to the place of the king Moshiach in the time of exile (before [the status of] "behold he is certainly Moshiach"). Therefore, while he is still in exile (for there he sits and waits and anxiously looks forward to redeeming the Jewish people, and the Divine Presence with them in exile) the king Moshiach builds a Temple (in microcosm). This is an illustration and example of the Temple in Yerushalayim (like "the synagogue of He slipped and settled," "that the Temple traveled and settled there."). [This settling serves] as a preparation for the future Temple, which will be revealed there first, and from there return (with G-d and the Jewish people) to Yerushalayim.
...Perhaps it can be said that the statement in the Midrash, that "at the time when the king Moshiach comes, he will stand on the roof of the Beis HaMikdash [Temple] and announce to the Jewish people, saying, Humble ones, the time for your Redemption has arrived," refers to the roof of the Beis HaMikdash which is the Temple in microcosm outside the land, which takes the place of the Temple in Yerushalayim ("The Temple traveled and settled there"). [This may be said] because after the future Temple is revealed and descends to the earth below, there is no need to announce to the Jewish people that "the time for your Redemption has arrived."
...The above can be applied to "The House of our Rebbe in Bavel" of our generation, the house (the synagogue and study hall) of my sainted father-in-law, the leader of our generation:
...In this generation, the last generation of exile and the first generation of Redemption, "our actions and Divine service during the time of exile" to make the lands of the nations into the land of Israel even in the lowest possible place, that is, the lower hemisphere (where the Torah was not given) has been concluded and completed. Through the elevation of the lowest possible place all the other lands of the nations are also elevated.
This [objective] is achieved through "Beis Rabbeinu" [Our Rebbe's House] in the lower hemisphere, from which light goes out to all the world, to make the whole world (until the furthermost corner of the world) into the land of Israel. This is the concept that "In the future the land of Israel will extend into all the lands," and "In the future, Yerushalayim will extend over all the land of Israel." For then there will be established a connection between all the synagogues and study halls throughout the entire world and the Beis HaMikdash. [This will occur] in the true and complete Redemption through our righteous Moshiach, the leader of the generation, who is the Moshiach (the Redeemer of Israel) of the generation. Further, and this is also essential, he is the leader of the Torah of Chassidus, since through the spreading outward ("when your wellsprings spread forth," until there is nothing beyond, to all corners of the world) is achieved the coming of the king Moshiach.
Therefore the greatness of "Beis Rabbeinu" can be understood. It is the essential "Temple in microcosm" of the final exile, "that the Temple traveled and settled there." Therefore, it is the actual place of the Temple of the future; not only that, but the future Temple will be revealed there, and from there return to Yerushalayim (as mentioned above).
