Reconstruction of the temple?
Summary
The Lord never said that the temple in Jerusalem would be rebuilt, but that it would be left desolate. Daniel also says that there will be desolation until the end.
According to the doctrine of Pre-Tribulation Rapture, there will be a future third temple on the Temple Mount in Jerusalem because this is predicted in several passages in the Bible. This temple will be approved by God.
Answer
The Lord Jesus never said that the temple in Jerusalem would be rebuilt, rather he said the opposite, namely that the temple would be left desolate or destroyed:
Mat 23:36-39 36 Truly, I say to you, All these things will come upon this generation
37 O Jerusalem, Jerusalem, the one who kills the prophets and stones those who are sent to her, how often I wanted to gather your children together, as a hen gathers her chicks under her wings, but you were not willing!
38 Behold, your house is left to you desolate.
39 For I say to you: You shall see Me no more until you say, Blessed is He who comes in the name of the Lord!
Mat 24:1-2 1 And Jesus went out and departed from the temple, and His disciples came up to show Him the buildings of the temple.
2 But Jesus said to them, Do you not see all these things? Truly, I say to you, not one stone shall be left here upon another, that shall not be thrown down.
(See also parallel passage Luk 13:35).
In Mat 23:37 and 38 the Lord says that he wanted to gather Israel to himself, but they did not want to; they rejected the Messiah, Jesus Christ. Therefore their house, the temple, would be left desolate, i.e. destroyed - as the Lord foretold.
This was literally fulfilled in a dramatic way in 70 AD, when the Romans under Titus destroyed Jerusalem and the second temple, and not one stone of the temple was left upon another.
Verse 39 speaks about the second coming of the Lord, his visible return (also according to the doctrine of Pre-Tribulation Rapture).
Verse 39 is linked to verse 38 by the word "for": It is therefore obvious that the temple will remain desolate until the return of the Lord and will therefore not be rebuilt before the return of Christ.
If the claim that the temple will be rebuilt before the Second Coming were true, then one has to question it: Why does the Lord only speak about the destruction of the temple and his return at this crucial point, but nothing about the rebuilding of the temple?
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The prophet Daniel also proclaimed this destruction about 600 years before the prophecy came true:
Dan 9:26 And after sixty two weeks, ‹the› Messiah [or: the/an anointed one] shall be cut off, but not for Himself. And the people of a coming ruler shall destroy the city and the sanctuary. And its end shall be with a flood, and desolations are determined, and there shall be war until the end.
On the one hand, Daniel clearly says that there will be desolations until the end. On the other hand, nowhere does he say that the temple will be rebuilt before the end.
The time of the end is defined in Dan 12:
Dan 12:13 But you, go on to the end, for you shall rest and stand for your inheritance at the end of the days.
The Lord's Olivet Discourse (end-time discourse) also clearly defines when the end will come:
Mat 24:13-14 13 But he who endures to the end shall be saved.
14 And this gospel of the kingdom will be preached in the whole world as a testimony to all the nations, and then the end will come.
----> The end is the visible return of Christ. Consequently, no temple will be built before the return of Christ.
Aspirations to rebuild
In Israel, advanced preparations are underway to build the Third Temple as soon as possible and to resume the temple service. However, this is controversial, as many in Israel believe that only the Messiah will build the temple when he returns.
They want to rebuild the temple on the same spot on the Temple Mount in Jerusalem where the first temple once stood, which was built by King Solomon. The second temple, which was built under Zerubbabel, also stood on the same site. But today the Islamic Dome of the Rock (the Omar Mosque) with its golden dome stands on this very spot.
But even if it were possible to build a third temple on the Temple Mount before the return of Christ, which cannot be completely ruled out, it would still only be the idiosyncratic work of men. Most Jews today are far from calling out to their crucified, risen and returning Messiah:
“Blessed is He who comes in the name of the Lord!”