There will never be a third Temple built on the original Temple Mount.
Ezra 6:14-15 the Jews did not build the second Temple according to the vision Ezekiel received, Ezekiel 40-48. Instead, God commanded his prophets Haggai, Zechariah and Malachi not to build the Temple according to Ezekiel's vision because it was intended to be an everlasting edifice connected with everlasting redemption, something the Israelites were not ready to receive after their exile from Babylon.
When the Jewish people emerged from exile at the decree of Babylon's King Cyrus their repentance was only partial and many of the Jews remained under foreign rule. The second Temple was built under Ezra’s leadership and Israel continued practicing Judaism and their Temple was desecrated as part of an effort to impose Greek-oriented culture and customs on the entire population. Roman rule refurbished the temple as Herod, Romans vassal king, rules the land of Israel. In 70 A.D. the Temple is once again destroyed. The Temple Mount was taken over in 691 A.D. as the Arab nation built the Dome of the Rock and there has not been any other Temple built since that time on the original Temple Mount.
The cornerstone for the new Temple was brought to Jerusalem on May 21, 2009 and still remains on the street. "Jerusalem Day" in 1967 was to celebrate the liberation of the Temple Mount, but there is a problem there as the Dome of the Rock sits on the Temple Mount. Baruch Ben-Yosel , chairman of the Movement to Restore the Temple, made it clear that the Temple had to be built in the exact spot where the Dome of the Rock sits.
There will never be a third Temple built by hands, Acts 7:48; Acts 17:24. When the veil of the Temple was torn from top to bottom after Jesus gave up the ghost, Matthew 27:50, 51, this symbolized that the sacrifice of Jesus and the shedding of his blood was now made for the atonement of sin and that all, Jew and Gentile, can come before Him as He is the only way to the Father, John 14:6.
There is no more veil for the Priest to enter into the Holy of Holies once a year to make atonement for Israel's sin, nor is there any more animal sacrifices as we are no longer under the Old Covenant nor the preaching of the law, but are under a new and better covenant of Gods grace through Christ Jesus as our High Priest, Hebrews 4:14-16. Jesus prophesied of the Temple being desolate and that no one will see Him again until His time comes meaning when He returns on the last day, Matthew 24:1, 2; Luke 13:34, 35, John 6:40.
God no longer dwells in a Temple made by hands, Acts 7:48, 49, and this is why God left it desolate all these years when it was destroyed by the Romans in 70 AD, Hebrews 9:11-28; 10:1-4. Now the Dome of the Rock sits on the Temple Mount and was built around 692 AD. The Muslims will never give it over to Israel, plus the Dome of the Rock is being refurbished for the son of perdition (not a Muslim man) to come and sit on his throne on the very Temple Mount of God and will cause a great falling away from truth, Isaiah 14:12-14; 2 Thessalonians 2:3-12.
Jesus fulfilled everything the temple stood for being the last sacrificial lamb taking away all the sin of the world. God no longer dwells in a temple made by hands, Acts 7:48-50; 17:22-31; Hebrews 10:7-18
Malachi 1:11 For from the rising of the sun even unto the going down of the same my name shall be great among the Gentiles; and in every place incense shall be offered unto my name, and a pure offering: for my name shall be great among the heathen, saith the LORD of hosts.
John 4:21 Jesus saith unto her, Woman, believe me, the hour cometh, when ye shall neither in this mountain, nor yet at Jerusalem, worship the Father. 22 Ye worship ye know not what: we know what we worship: for salvation is of the Jews. 23 But the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth: for the Father seeketh such to worship him. 24 God is a Spirit: and they that worship him must worship him in spirit and in truth.
The church, (body of Christ) is the temple where God dwells by His Holy Spirit, Zechariah 6:9-15 (prophecy of coming Messiah); 1 Corinthians 3:16, 17; Ephesians 2:19-22, Galatians 3:19-29.
In 70AD the second temple was destroyed and put an end to the temple made by hands and the sacrifices made there. The Temple of God now dwells in all who are Spiritually born again and indwelled with the Holy Spirit, John 3:5-7; Romans 10:9, 10.
God no longer honors the blood sacrifice of unblemished animals as through Christ who suffered and died for all has already made the ultimate blood sacrifice for the atonement of sin, John 14:6; Ephesians 2:8.
Hebrews 10:
1 For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. 2 For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. 3 But in those sacrifices there is a remembrance again made of sins every year. 4 For it is not possible that the blood of bulls and of goats should take away sins. 5 Wherefore when he cometh into the world, he saith, Sacrifice and offering thou wouldest not, but a body hast thou prepared me: 6 In burnt offerings and sacrifices for sin thou hast had no pleasure. 7 Then said I, Lo, I come (in the volume of the book it is written of me,) to do thy will, O God. 8 Above when he said, Sacrifice and offering and burnt offerings and offering for sin thou wouldest not, neither hadst pleasure therein; which are offered by the law; 9 Then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second. 10 By the which will we are sanctified through the offering of the body of Jesus Christ once for all. 11 And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins: 12 But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God; 13 From henceforth expecting till his enemies be made his footstool. 14 For by one offering he hath perfected for ever them that are sanctified. 15 Whereof the Holy Ghost also is a witness to us: for after that he had said before, 16 This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; 17 And their sins and iniquities will I remember no more. 18 Now where remission of these is, there is no more offering for sin.