By Rabbi Berach Steinfeld
Posuk chof aleph in Perek Tes Zayin in Chumash Devarim tells us that one may not plant a tree next to the Mizbeach of Hashem. Rashi explains that this teaches us that one may not plant a tree or build a house on Har HaBayis. The Chinuch in Mitzva taf tzadik bais argues with this and says the issur applies just to the azarah.
The Yalkut Shimoni says that the posuk includes the issur of building a Sukkah next to the Mizbeach of Hashem. The Panim Yafos explains that this would include a Sukka for Sukkos in which the Kohanim would eat the Lechem Hapanim as well as the leftover menachos that should have also been eaten in the Sukkah; but was eaten in the azarah due to the fact that it was prohibited to build a Sukkah there. Since one may not build a Sukkah in the azarah, they are rendered pattur from Sukkah. The Yalkut Shimoni teaches us that one has a chiyuv to make a Sukkah for himself and for hekdesh as it says make a Sukkah for yourself and it also says make a Sukkah seven days for Hashem? If we just stated that building a Sukkah is prohibited, it seems to contradict that premise! The Panim Yafos clarifies this by saying that making a Sukkah for Hashem is referring to eating the breads of the Toda, which is eaten within the boundaries of Yerushalayim. That would require a Sukkah and one would be allowed to build it since it is outside the boundaries of the Bais Hamikdash.
We find that the Sifri says that one may build a Sukkah even in the azarah. How do we reconcile this with the above Yalkut that says there is no Sukkah in the BaisHamikdash? One way of answering is that it would depend if we hold like Reb Yehuda that a Sukkah is a diras keva. If we do, then it would not be allowed in the azarah. However, if you hold like the Chachamim that a Sukkah is a diras arei then it would be permissible to build it in the Bais Hamikdash. Some want to argue and say that the minute the Sukkah is built for the Mitzvah it is considered a keva similar to the halacha in Tefilin that the kesher does not need be a kesher shel kayoma; nevertheless, one may not make this kesher on Shabbos because the mitzva makes it into a keva, additionally, we could answer that really for Sukkos one is allowed to build a Sukkah for the purpose of eating Kodshim. The issur they bring down of building a Sukkah applies to the rest of the year where there is no mitzvah in Sukkah. This would fit in with the posuk in Sefer Nechemya, Perek Ches that says they built Sukkos each person on their respective roof and in the courtyard of the Bais Hamikdash. We see from this that one may build a Sukkah in the Bais Hamikdash.
May we be zocheh to see the Bais Hamikdosh be rebuilt and we will find out whether or not there will be a Sukkah in the Bais Hamikdosh during Sukkos.