"Will Israel rebuild the temple in Jerusalem now that it's the capital again?"
My answer won’t be what you expect.
As I read the Bible in both Greek and Hebrew, I see strong evidence for sacrifices or offerings starting again, but I see no Third Temple until after the Messiah arrives.
Let’s analyze the Hebrew and Greek words used in key passages to determine what we will see.
Beit is the Hebrew word for house or temple. Prophetically the Temple is referred to as the Lebanon because of the cedar wood needed to build it. In key Bible passages the Hebrew word Heikhal, which could mean tent, wedding chuppah (covering), or palace.
Sound of tumult from the Ir, a sound from the Heikhal [most mistranslations use Temple], a sound of Hashem that rendereth gemul (retribution) to His enemies. Isaiah 66:6 (OJB)
Hineni, I will send malachi, and he shall prepare the Derech before me: and HaAdon (the L-rd [Moshiach] Zech 4:14), whom ye seek, shall suddenly come to His Heikhal [most mistranslations use Temple], even the Malach HaBrit, in whom ye have chafetz (delight): hinei, He is coming, saith Hashem Tzva’os. Malachi 3:1 (OJB)
And speak unto him, saying, Thus saith Hashem Tzva’os: Hinei Ish, TZEMACH Shmo ; [Yehoshua is said to be the namesake of the coming Moshiach Ben Dovid; see Ezra 3:8 for the Aramaic translation of Yehoshua’s name, Yeshua; see Jer 23:5; 30:9; 33:15; Ezra 3:8; Zech 3:8; Mt 2:23; Isa 4:2; 9:2-7; 11:1-12; 53:2, 11; Moshiach the new “Joshua” Isa 49:8].]; and out of his place yitzmach (he [Moshiach] shall sprout up, Yeshayah 53:2), and he shall build the Heikhal Hashem. It is he who shall build the Heikhal Hashem; and he shall carry hod (majesty), and shall sit and rule upon his throne; and he shall be a kohen [Tehillim 110:4] upon his throne; and the atzat shalom (counsel of peace) shall be between them both. And the atarot (crowns) shall be to Chelem, and to Toviyah, and to Yedayah, and to Chen ben Tzephanyah, for a memorial in the Heikhal Hashem. And they that are far off shall come and build the Heikhal Hashem, and ye shall know that Hashem Tzva’os hath sent me unto you. And this shall come to pass, if ye will diligently obey the kol (voice) Hashem Eloheichem. Zechariah 6:12–15 (OJB)
In the Messianic Scriptures, the two Greek words used are Heiron for Temple or Temple buildings on the Temple Mount and Naos for the Holy of Holies, whether in Heaven or on the earth.
Heiron is used frequently in many books, but only Naos is used in 2 Thessalonians 2 and ALL of Revelation. This means we’re not talking about a building during the final seven years of tribulation. We’re talking about a reserved Holy area where only the High Priest goes into and only on Yom Kippur.
Let no one in any way lead you astray, because, unless the Merid (Rebellion, Revolt, the [Anti-Moshiach] Shmad Betrayal Defection of Apostasy, the Azivah Abandonment) Desertion comes rishonah (first), and the Apocalypse of the Ish HaMufkarut (Man of Lawlessness), the Ish HaChatta’ah Ben HaAvaddon (Man of Sin, Son of Destruction Anti-Moshiach) is unveiled. I’m referring to the one setting himself against and exalting himself AL KOL EL (above every G-d, DANIEL 11:36), above all that is given the appellation "G-d" or object of worship, with the result that in the Beis Hamikdash Heikhal he sits down on the MOSHAV ELOHIM (throne of G-d, YECHEZKEL 28:2), proclaiming that he himself is Elohim... 2 Thessalonians 2:3–4 (OJB)
Please notice how Dr. Phillip Goble, the author of the “Orthodox Jewish Bible” translated Naos for Heikhal above? Brilliant!