Rabbi Yehuda Zolden brought a number of sources, that up to 54 years after the destruction of the Second Temple, an altar was still present there and in the days of Rabban Gamliel of Yavneh, one generation after the Temple's destruction, they still brought the Passover sacrifice upon this altar (See, Pesachim 74a, the writings of Maharatz Chiyut page 618, Sanhedrin 11b, Beitza 22a, Yerushalmi Taanit 2:5, Netziv, He'amek Davar, Dvarim 16:1-3).
Concerning Rambam, it is unlikely that he offered the Passover Sacrifice, since he made it a private holiday for himself, when he was able simply to visit the Temple Mount, but he makes no mention of offering the sacrifice which is a much greater religious accomplishment. It is also highly unlikely that the Moslems would have let the Jews put up an altar on the Temple Mount during Rambam's time.