I doubt that the dome of the rock is on the Temple Mount, but do you have a link? I can change my mind. lol Probably won't though.
The Dome of the Rock actually was a church, before it was a Muslim Shrine.
I haven't really looked at this topic for awhile, but from my understanding the Romans destroyed the Jewish Temple in 70 A.D.. So, where did all these Roman soldiers stay? At a Roman Fort right?
If the Romans destroyed the Temple, why is the Temple Mount still intact?!?! Que Jeopardy music....
I'm just spouting stuff off from memory, so make corrections where applicable. The Temple Mount is at the City of David. I believe this is the video that explains everything, if not watch some more.
From memory, I believe it was said, that the the rock inside the dome (previously a church) was where Jesus was sentenced to death. Please correct me If I'm wrong again. What else? umm I don't know.
Back to Mathew 24
1 And Jesus went out, and departed from the temple: and his disciples came to him for to shew him the buildings of the temple.
2 And Jesus said unto them, See ye not all these things?
verily I say unto you, There shall not be left here one stone upon another, that shall not be thrown down.
Here is a picture of the City of David. Not much left right? Anyways, this is just what I believe. Everyone is entitled to believe what they want.