I can assure you that Jews would not be permitted to built a synagogue, let alone The 3rd Temple in Mecca or Medina. They will not allow Jews to enter those cities, the centers of the Haj (Muslim pilgrimage). Interesting note is that Medina was a Jewish city until Mohammed slaughtered all the Jews in it. Islam has been a religion of blood since its very beginnings.
Law expanding definition of terrorist activity passes first Knesset reading (Haaretz)
from the article: Israel fears violence following arrest of Islamic Movement head