This is a very interesting question to receive because it actually has quite a few answers, depending on how you want to approach it. Before we can really dive in an answer it, though, we need to address some of the presuppositions that such a question is – generally speaking – bringing to the text.
The Foundation of The Question
The question is a natural outcropping of Dispensationalist Pre-Millennial theology, which holds that, “the Third Temple will be rebuilt when the Antichrist, often identified as the political leader of a trans-national alliance similar to the European Union or the United Nations, secures a peace treaty between the modern nation of Israel and its neighbors following a global war. The Antichrist later uses the temple as a venue for proclaiming himself as God and the long-awaited Messiah, demanding worship from humanity.”1
This theology – which asserts that the antichrist is some kind of political leader who will form a one-world-government, bring universal peace and prosperity, bring about a one-world currency, and then declare himself a god – is actually not Biblical at all. All of these ideas and notions of the antichrist are not found in scripture, but are actually found in a fictional theological-thriller book series by Tim LaHaye and Jerry B. Jenkins called Left Behind.
While there is some tenuous – and I stress tenuous – Biblical support for some of the ideas (all of which require doing a large amount of violence to the texts), the majority of them actually come from a gentleman by the name of John Nelson Darby2, a 19th century Bible teacher with no actual theological training.
This view of Eschatology (the study of the end of things) is only about 150 years old but is incredibly popular and widespread in American Evangelicalism.
Will A Third Temple Be Built?
There are a few answers to this, depending on how you think about it.
In general, the answer to the question is No. There will not be a third temple built, and if there is a third temple it will have absolutely no Biblical significance whatsoever.
But, depending on how you look at the scriptures and define antichrist, there could be other answers.
Why Would The Pope Do This?
The Lutheran Confessions maintain that the Pope is the Antichrist.
That being the case, the real question is: Why would the pope build a new Jewish temple on the temple mount? He probably wouldn’t.
The Third Temple Exists Already
The Muslims can also be seen as a type of antichrist. In which case we can consider the third temple to have already been built in the form of The Dome of The Rock – the antichrist has already built his temple.
The Actual Third Temple
The actual third temple, though, is Jesus Himself. He said, “Tear this temple down and I will rebuild it in three days,” and was speaking of Himself. Furthermore, the temple – outside of the Gospels and the book of Acts – is repeated referenced as the human heart. Essentially, we as Christians, are the third temple.
So in this way, the third temple has already been built. Just not on the temple mount in Jerusalem, but in our hearts as Christians.
Hope this helps!
Footnotes
1: https://en.wikipedia.org/wiki/Third_Temple#Dispensationalist
2: https://en.wikipedia.org/wiki/John_Nelson_Darby