It is possible that it would not even be necessary to build the third temple on the so-called "Temple Mount". There are some who have theorized that the temple mount, being about the same size and shape as a typical Roman fort, is exactly that, a fort named Fort Antonia which has never been found, and is in fact "hidden in plain sight" as it was misidentified by ignorant Crusaders who did not know what they were looking at centuries later. The temple itself, was located a few hundred feet south-east of the fort, and was thoroughly demolished by the armies of Titus, as described by Josephus in his writings. You can research this theory by looking for the works of the late Ernest L Martin, or a more recent researcher, Robert Cornuke. A controversial theory, no doubt, but certainly within the realms of possibility.