Orthodox Jews differ as to when and how the Third Temple should be rebuilt.
One school of thought says, that the Temple will descend in fire from heaven completely built after a religious government is established as the Messiah arrives in the Age of Redemption.
According to another Orthodox school of thought, the Messiah, an earthly, Jewish king, will build the Third Temple. And, in fact, they state that the only conclusive proof of the identity of the Messiah is that he will be the one to build the Temple.
They believe;
The Messianic King will arise in the future and restore the Davidic Kingdom to its former state and original sovereignty and that He will build the Sanctuary and gather all the dispersed of Israel.
With regards to Deuteronomy 30:3-5
According to the majority of Orthodox Jews this prophecy has never yet been fulfilled, thus must relate to the Messianic redemption.
"I also will do this unto you; I will even appoint over you terror, consumption, and the burning ague, that shall consume the eyes, and cause sorrow of heart: and ye shall sow your seed in vain, for your enemies shall eat it. And I will set my face against you, and ye shall be slain before your enemies: they that hate you shall reign over you; and ye shall flee when none pursueth you". Leviticus 26:16-17