A third Temple is not mentioned in the Torah
We hear how a gentile told Rabbi Eliezer that the people of Yisrael were not close to God, citing various kinds of evidence, whereupon the Rabbi turned him into a heap of bones. Rabbi Eliezer recounts the answers that Elijah once gave him when he raised the same issues as the gentile. We hear an explanation of the First and Second Temples, and how God will reveal the Temple at the time of the final redemption.
The final Temple will not be a physical structure erected by the hand of man. Rather, it's a spiritual and physical Temple actualized by the will of God in the moment we complete our correction. Any structure in our world that does not include the workmanship and Light of God is doomed to destruction.
This dissertation imbues all of our endeavors, all that we build, with the sacred craftsmanship of the Creator. The spiritual foundation, columns, and pillars of the Temple rise up in this passage. And although our eyes do not observe its construction, the Light generated by its presence illumines the planet, banishing forces of darkness, sin, death, and destruction. The Final Redemption unfolds with great kindness, for this ancient book is a book of kindness; and its every page bespeaks compassion, mercy, and leniency.