On top of the remains of the Jewish temple erected in the B.C. era?
No, not really. The Aqsa mosque -- which is the 3rd holiest site in Islam -- was built on the site of a ruined and abandoned Byzantine church, which was itself built on the site formerly occupied by the Royal Stoa, a secular building on the Temple Mount built by Herod. It was built adjacent to the Second Temple, not on top of it.
You're probably thinking of the other mosque on the Temple Mount, the Dome of the Rock, which WAS built on the Temple site between 689 and 691 AD. Although it should be noted that when the Arabs got to Jerusalem, the actual Temple site had already been desecrated by a temple to the Roman God Jupiter.