Minchat Chinuch, on Mitzva 95 : We need to Know How to Construct the Temple Vessels
Now behold Rambam here in chapter 3 wrote about the structure of the Menora very clearly, and also the structure of the Showbread Table, and regarding the structure of the incense altar, he is somewhat brief, and he also wrote a bit on the structure of the Kiyor {Laver}, see there. Yet regarding the structure of the ark he did not write anything at all. And it is obvious that all these vessels were all the time different, for in the Second Temple, they did not have vessels from the First Temple, and in the days of the Hasmoneans all the vessels that were there were lost as explained in Menachot 28b that they first made the Menora out of iron, then they became richer, etc. If so we have to know the laws. And even today it is possible that if the Kingdoms will give us permission to build the Temple, it is a mitzvah to build, as explained in the Midrash [Breishit Rabba] that in the days of Rabbi Yehoshua the son of Chanania they gave permission and they started to build, and see also the book Capot Temarim that Rabbeinu Yechiel, one of the masters of Tosafot, wanted to go and offer sacrifices in Jerusalem; if so this rule applies also to the building of the Temple
{end of translated quotation}.
A few sentences later, Minchat Chinuch deals with the question, is this true for the ark, because we know that in the 2nd Temple they did not make a new ark to replace the ark that was hidden away during the time of the First Temple. I will leave aside that discussion for now.