The two main groups I know of are the 'Temple Institute' and the 'Temple Mount Faithful'. They have been making many of the items necessary for the Temple, and their belief is that it will be rebuilt on the Temple Mount. Their websites:
http://www.templeinstitute.org/
http://www.templemountfaithful.org/
A good site for Temple Mount related articles is: http://www.templemount.org/ There are a number of interesting articles and links on that page, especially concerning exactly where the original Temple was located on the Mount. Everyone says the Dome of the Rock covers it, but Tuvia Sagiv, a Tel Aviv architect and researcher, says different. His evidence is very compelling, and definitely worth reviewing. According to his research, the Holy of Holies was located under the current Fountain in the plaza south of the mosque. That is where many muslims was their feet before going to pray. Since the entire current Mount is actually of Roman construction built on fill, the original level is many meters underneath it. Interesting enough, his positioning of the Holy of Holies is directly in line with the Kotel prayer site. If he is correct, which it seems from the evidence he is, when Jews pray toward the wall, they pray directly facing the exact position of the Holy of Holies.
Dr. Jones, and others, believe that the Ark and original Tabernacle are to be re-placed at Gilgal, as it was before Solomon built the Temple. I had never heard this view before, and his explanation of it, with biblical backing, is very interesting and thought provoking. He has rabbinical advice and consent on everything he does, so it's not just his idea.