There never was a 1rst or 2nd Temple at this cite. Just think of the mind set of a Jew who believes a Jewish temple was here. Although there is every indication that Fort Antonia was and still parts of on this location.
3. TM has been A Muslim Place of Prayer for over 1300 YEARS!!!
Haram esh-Sharif(Dome of The Rock) and the Al Aqsa Compound is A MUSLIM place of worshipping since 692 CE. It is NOT a temple mount, where jewish temple once was. Before that it was a place where people of Jerusalem brought their GARBAGE. It was A Filthy Garbage Depot. Not a single JEW, not a single Muslim...NOBODY cared for this place...until a muslim ENTREPRENEUR offered to build a place to pray. Umayyad Caliphs commissioned the construction of the al-Aqsa Mosque and Dome of the Rock on the site. The Dome was completed in 692 CE, making it one of the oldest extant Islamic structures in the world. SO...jews have absolutely ZERO reasons to pray there. BUILD a NEW Temple and enjoy your prayers.