First, JTA has an article on the Temple Insitute: Holy work or troublemaking? Laying the groundwork for a Third Temple in Jerusalem. Excerpt:
“Our goal is to fulfill the commandment of ‘They shall make a Temple for me and I will dwell among them,’ ” [Rabbi Chaim] Richman says, quoting Exodus. “The basis of a Torah life is action.”Related: Tisha B'Av Temple Video Gains 35,000 Views (Arutz Sheva).
Following the Second Temple’s destruction in 70 C.E., most rabbis adopted the position that Jewish law prohibits reconstructing the Holy Temple prior to the age of messianic redemption, or that the law is too ambiguous and that the messiah must come first.
The Temple Institute takes a different position.
“There are no Jewish legal barriers” to rebuilding the temple, Richman says, only political ones.
The institute isn’t shy about advocating what many see as a radical goal: replacing the mosque at the Dome of the Rock with a new Jewish Holy Temple. A painting in the institute’s exhibition depicts this scenario, with the city’s light rail line taking residents to the Temple Mount. The Temple Institute is dedicated to laying the groundwork for this vision.
The organization has formulated a program for where the temple will stand and what its vessels will look like, aided by 20 men who study Temple law full-time. The products of this research — 40 ritual objects — are on display in Plexiglas cases at the institute’s headquarters in the Old City.
My understanding is that the Temple Institute advocates the rebuilding of the Temple when the Messiah comes, which is not made clear in the JTA article. For more on the Institute and my own views regarding its goals, see here and links. Related more recent thoughts are here.
Also, at the Israel's History: A Picture a Day blog: A Tisha B'Av Special: Are These the Beams of the Temple? Is this the Gift from King Hiram of Sidon to King Solomon? New, 85-year-old photos of some of the beams from the IAA. (HT Dorothy Lobel King. Background here.)