Red heifer is the very least of the problems connected to the Third Temple.
While a true red heifer may be somewhat rare, there is a misunderstanding that such is so difficult to find. There have only been nine slaughtered and burned because that was all that were necessary, not because only nine were ever found.
“Red heifer is the very least of the problems connected to the Third Temple.”
Agreed. There is that not so small issue of the Al Aqsa Mosque and the Dome of the Rock existing on what is now the Temple Mount.
By all accounts, the 1st and 2nd Temples were there first but that means little or nothing to the Muslims who built both structures there.
IIRC correctly (and I may be wrong) the Al Aqsa Mosque and Dome of the Rock would need to be removed before the Third Temple could be constructed. If that happens, the you know what is majorly going to hit the fan in all directions.