Did God still dwell in the temple while Jesus was on Earth?

This is just a question that has intrigued me and I can't think of a definite answer. I understand that the presence of God dwelt first in the Tabernacle and then in Solomon's temple in Jerusalem. God promised to dwell with His people as long as they were faithful to Him, but Israel rebelled. God allowed them to be taken captive by the Babylonians who then destroyed the temple as well. Also, [Ezekiel](http://www.biblegateway.com/passage/?search=Ezekiel+10&version=ESVUK) talks about God's presence leaving the temple due to Israel's unfaithfulness. Israel is eventually restored and the priesthood continues, as well as the temple and sacrificial system. God promises countless times about the full restoration of the temple, obviously pointing forward to Jesus. So my question: **Did God's presence ever return to the temple in post-exile Israel?** If so **Was God's presence still dwelling in the temple while Jesus was on Earth?** I'm sorry my Scripture references are lacking, I hope this question makes sense.