423. No Roof; The Temple
Tefillin, Mezuzah v’Sefer Torah 6:5
A house without a roof does not require a mezuzah. If part of it was covered by a roof and part was not, then it seems to me (says the Rambam) that if the covered part is near the entrance, it requires a mezuzah. The doors should be attached to the building before the mezuzah.
Tefillin, Mezuzah v’Sefer Torah 6:6
The Temple Mount, its chambers and courtyards, and entrances to shuls and study halls that do not have apartments for tenants do not require mezuzos because they are sanctified. A shul in a small town where guests stay over requires a mezuzah. Similarly, a shul in a big city that has an apartment requires a mezuzah. None of the gates to the Temple had mezuzos except for the Nicanor Gate and those further inside, and the entrance to the Parhedrin chamber because this was where the High Priest lived for seven days when he was separated from his wife prior to Yom Kippur.