JOEL - Joseph Smith said:

"Judah must return, Jerusalem must be rebuilt, and the temple, ..... 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." (TPJS, p. 286, Documentary History of the Church, vol. 5, p. 337.) (Zech. 2:12; 12:6; Ether 13:5, 11; 3 Ne. 20:29-36; D&C 77:15)

The keys to gather "Israel from the four parts of the earth" were bestowed upon Joseph Smith by Moses during his appearance in the Kirtland Temple on April 3, 1836.
In 1840-1841, Orson Hyde, an apostle, was commissioned by the Prophet to go to Jerusalem and dedicate the land. His prayer petitioned for the gathering home of the exiles, the fruitfulness of the earth, the establishing of an independent government, the rebuilding of Jerusalem, and "rearing a Temple in honor of thy name".
When Elder Hyde offered that dedicatory prayer, there were fewer than 5,000 Jewish people in the entire land of Palestine. Today there are over 2,250,000, and they have literally come from the four corners of the earth-from over 100 separate nations-and this in fulfillment of the prophecies.

But before the temple is built, the Jewish people will begin to believe in Jesus Christ and eventually the gospel will be preached to them:

"And I will remember the covenant which I have made with my people; and I have covenanted with them that I would gather them together in mine own due time, that I would give unto them again the land of their fathers for their inheritance, which is the land of Jerusalem, which is the promised land unto them forever, saith the Father. And it shall come to pass that the time cometh, when the fulness of my gospel shall be preached unto them; And they shall believe in me, that I am Jesus Christ, the Son of God, and shall pray unto the Father in my name." (3 Nephi 20:29-31)

Wilford Woodruff said in 1855: "When the Gentiles reject the Gospel it will be taken from them, and go to the House of Israel, to that long-suffering people that are now scattered abroad through all the nations upon the earth, and they will rebuild Jerusalem their ancient city, and make it more glorious than at the beginning, and they will have a leader in Israel with them, a man that is full of the power of God and the gift of the Holy Ghost; but they are held now from this work, only because the fulness of the Gentiles has not yet come in." (Journal of Discourses, vol. 2, p. 200.)

President Woodruff also identified who will build the temple when he said:
". the time is not far distant when the rich men among the Jews may be called upon to use their abundant wealth to gather the dispersed of Judah, and purchase the ancient dwelling places of their fathers in and about Jerusalem, and rebuild the holy city and temple." (Millennial Star, vol. 41, p. 244.)

Orson Pratt said:
"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." (JD, vol. 19, p. 20. Italics added.)

Considering all scriptures and statements it appears that after the Gospel has been preached to the Jews they will rebuild the temple and will expect their "true Messiah" to come to them. When He does come He will reveal to them that He is the same one called Jesus Christ whom they did not recognize as the Messiah when He first came:

". they shall look upon me whom they have pierced, and they shall mourn for him. " (Zech. 12:10.)

"And then shall the Jews look upon me and say: What are these wounds in thine hands and in thy feet?
Then shall they know that I am the Lord; for I will say unto them:
These wounds are the wounds with which I was wounded in the house of my friends. I am he who was lifted up. I am Jesus that was crucified. I am the Son of God.
And then shall they weep because of their iniquities; then shall they lament because they persecuted their king." (D&C 45: 51-53.)