Correct.
The First and Second Temples were on the Temple Mount.
So, too, shall be the Third.
So, which 1st, 2nd, and 3rd Temple are you talking about?
(BTW, I'm pretty sure I've missed some of the Temples in a long series of Temples ~ then there's the Temple where the Samaritans made sacrifice ~ )
AND so too, the 4TH TEMPLE, which shall be the everlasting Temple, and Y'shua ha Mashiach will reign from there for a 1000 years!!! MARA NATHA!!!
Correct.