The younger “traditional” students have been arguing otherwise. There already is some questioning otherwise as to the “exact” location of the previous temples.One could build it adjacent to the wailing wall some have argued.
Shlomo Goren, an IDF Chief Rabbi and Israeli Chief Rabbi, spent more time on the laws and layout on the Temple Mount than anyone for centuries.
Goren had been a build the Third Temple enthusiast until he got to study the Temple Mount close up immediately after the 67 war.
After he had done much close up study, in reaction to the activities of groups preparing for the Temple today by recreating the Temple garments and artifacts, Goren quoted the Book of Ecclesiastes: All is vanity and a striving after the wind.
No yeshiva bochurs get a say.