The temple will not be rebuilt, period.
After Christ returns the new Jerusalem is established in final form and we are told, "But I saw no temple in it, for the Lord God Almighty and the Lamb are its temple." Ezekiel's temple was a spiritual picture of the sacrificial work of Jesus Christ during this age as He has attoned once for all for the sins of His people (Matt. 1:21).
Even now there is no earthly temple because the true temple is in heaven (where it always was; Heb. 8:5). We inhabit the new Jerusalem, the heavenly Mt. Zion (Heb. 12:22). The earthly temple was just a temporary pattern to point the Old Covenant church to Christ. One He appeared the temple no longer served a useful purpose, and so God destroyed it so the people would not confuse the temporal/carnal with the eternal/spiritual.
But when you see Jerusalem surrounded by armies, then know that its desolation is near. Then let those who are in Judea flee to the mountains, let those who are in the midst of her depart, and let not those who are in the country enter her. For these are the days of vengeance, that all things which are written may be fulfilled. (Luke 21:20-22)Most of the church, including the 1st century Jewish believers, understands this fact. A segment of the premil camp does not, and so they still look for a future temple just like the apostate Jews who have missed the coming of the Messiah for the last 2000 years.
God brings Ezekiel, by vision, into the LAND OF ISRAEL. And he shows him the temple that will be built. When it is, it does not say. Could very well be during the Millenium because other passages speak of the nations of the earth coming to this place to worship the LORD.
You have a prederist view. The prederist declares every passage that is unexplained as spiritual and an allegory. They also do not interpret the bible literally, they believe all promises to Israel have been transferred to the Church (replacement theology), along with many other liberal denominations, and that God is finished with the nation of Israel.
God is not finished with Israel. They are the apple of his eye, no matter how rebellious and rotten they are. There is always a remnant. And as for the Temple... we will see. But one thing we do agree. That Christ is the Messiah and the author of our salvation. He is the bridge between man and God. There is no other way to God. Amen.