Anti-Christ in the temple of Solomon is considered one of the definitive signs to accurately measure the remaining time until the second coming of Christ. Once that it totally rebuilt then it's a matter of mere years. As far as the rapture goes, it's either post-tribulation or pre-tribulation. See the book of Revelations.
The Temple of Soloman was destroyed by the Babylonians centuries before Christ. The first temple that was desecrated was the second one built on the return from Babylon where Antiochus Epihaims set up a statue of Jupiter and sacrificed a Sow on the altar. He was defeated by the Maccabee brothers who cleansed and rededicated the temple. The event is commemorated by the festival of Hannakah known in Johns gospel as the Feast of the Dedication, (10:22) Jesus used this event to warn his Disciples and every believer of a future antichrist who would desecrate the temple. Thats why in Matthew it says let the reader understand. They were well aquainted with the history. What happened in the days of Maccabees was a type of what was to happen in the future using Rome and with the ultimate Antichrist in the last days.