The Jews anxiously await the day that they will be able to rebuild the Jerusalem temple, often referred to as the third temple, as a holy house of worship of God. There has been a Jewish institute established, The Temple Institute, in Jerusalem for the very purpose of researching the history of the temple and its eventual reestablishment on the temple mount, and making steps toward that end goal. The Jews plan to reinstitute or “restore” daily temple prayer and sacrifice, as was prophesied in the Bible, and they speak with fervor about the “restoration” of the divine service of worshiping Almighty God in His holy house. It is interesting that in ancient Israel the building of the temple was always directed very carefully by abundant revelation of God to His prophet on the earth. In a different sense, The Temple Institute today seeks understanding in ancient prophesy and tradition as found in the Torah to restore the architecture, vessels, ordinances, worship, and other characteristics that will accompany the temple of God. ((See a video of the restoration of the menorah, and the restoration of the crown of the high priest.))
The Latter-day Saints also see the reconstruction of a temple in Jerusalem as one of the signs of the times of the Second Coming of the Savior. Whether it will be built by the Church or the Jews or the Jews under the direction of the Church or will later come under the direction of the Church after the Jews are converted to Christ is unclear (Do you know of any studies clarifying this?). What is clear is that the saving ordinances of the restored gospel of Jesus Christ will be performed therein at some point, under the authority of the priesthood of God, as they are performed currently in 125 temples around the world.
Joseph Smith once taught:
What was the object of gathering the Jews, or the people of God in any age of the world? …The main object was to build unto the Lord a house whereby He could reveal unto His people the ordinances of His house. ((Joseph Smith, HC 5:423))
In addition to the scriptural prophesy, specifically in Ezekiel 40-48, consider the following quotations from latter-day prophets and apostles: ((Gathered from LDSLastDays.com, <http://www.ldslastdays.com/default.aspx?page=psc711.htm>))
Judah must return, Jerusalem must be rebuilt, and the temple, and water come out from under the temple, and the waters of the Dead Sea be healed. It will take some time to rebuild the walls of the city and the temple, Etc.; and all this must be done before the Son of Man will make his appearance. ((Joseph Smith, HC 5:337))
The work is moving on for the gathering of the Jews to their own land that they may build it up as it was in former times; that the temple may be rebuilt and the mosque of the Moslem which now stands in its place may be moved out of the way; that Jerusalem may be rebuilt upon its original site; that the way may be prepared for the coming of the Messiah, who shall be seen in the midst of those whose ancestors nailed him to the cross, and who, when they see the marks in His hands, shall say in answer to their inquiries, “These are the wounds with which I was wounded in the house of my friends.” ((CW Penrose, JD 24:217))
The twelve tribes will return to Palestine and rebuild Jerusalem and the temple before and preparatory to the coming of the Lord. But let us read a little further to show more fully that this was a work of the latter days. “And all nations shall flow unto it and many people shall go and say ‘Come ye and let us go up to the mountain of the Lord, to the house of the God of Jacob, and he will teach us of his ways and we will walk in his paths, for out of Zion shall go forth the law and the word of the Lord from Jerusalem.'” Two separate and distinct places. The whole of the twelve tribes of Israel are to return back to Palestine in Asia and rebuild their city of Jerusalem and a temple within that city before, and preparatory to the coming of the Lord. Ezekiel, in describing the latter-day building of Jerusalem, says, “And the name of the city from that day forward shall be ‘The Lord is there.'” After the rebuilding of that city it will never be forsaken, or plucked up. As Jeremiah says in his 31st chapter, “It shall never be plucked up or thrown down henceforth and for ever.” It will stand while all the generations of the earth shall stand when the house of Israel shall return and rebuild it under the direction of the Almighty. ((Orson Pratt, JD 14:349-50))
Then, when the Gentile nations shall reject this Gospel and count themselves unworthy of eternal life, as the Jews did before them, the Lord will say–“It is enough, come away from them, my servants, I will give you a new commission, you shall go to the scattered remnants of the house of Israel. I will gather them in from the four quarters of the earth, and bring them again into their own lands. They shall build Jerusalem on its own heap; they shall rear a Temple on the appointed place in Palestine, and they shall be grafted in again.” ((Orson Pratt, JD 18:177))
As I have been reading to you today, the Jews have got to gather to their own land in unbelief. They will go and rebuild Jerusalem and their temple. ((Wilford Woodruff, JD 15:277-79))
After the Jews have repented and received the Gospel, having ackowledged Jesus Christ as their Redeemer, the temple in Jerusalem will be built according to the prophecy in Ezekiel. ((Joseph Fielding Smith, Signs of the Times, 238))
By and by there will be a Temple built at Jerusalem. Who do you think is going to build it? You may think that it will be the unbelieving Jews who rejected the Savior. . . . The Temple at Jerusalem will undoubtedly be built, by those who believe in the true Messiah. Its construction will be, in some respects different from the Temples now being built. It will contain the throne of the Lord, upon which he will, at times, personally sit, and will reign over the house of Israel for ever. ((Orson Pratt, JD 19:20-21))
See more quotes and scriptures on the rebuilding of the temple in Jerusalem from LDSLastDays.com.