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

The answer is Yes, God's presence was in fact in the Second Temple, while Jesus was alive, and I'll give evidence, but there's an asterisk.
Wspier got it part right, but contradicts himself.
-- "I disagree with those who say God did indwell the second temple and cite as evidence the temple veil rending in two, claiming that indicates God's departure from the second temple." Here he says God did not indwell, inhabit the 2nd temple.

• "Rather, taking the temple veil at it's basic purpose, we realize the veil's purpose was not to "hold God in" the holy of holies, but rather to keep man out, lest anyone who enters dies. Even the chief priest, selected once a year by lottery, had much ritual cleansing (ablution) to perform so he would not be killed by entering into God's presence with any uncleanness." Here he says God did inhabit the Temple.
  The point being that Christ himself taught in the Temple and he explicitly said that the 2nd Temple in Jerusalem was His Father's House.
  Up until Christ's death on the cross for all humanity, the sacrificial system, and the Holy Place was still valid and in use, and the means by which sins were forgiven on the day of atonement.
  In fact, at the exact time the lambs were being slaughtered in the temple on Passover, Christ was crucified, - and he became our perfect spotless Passover lamb. Remember, that the curtain was torn, while Jesus Christ was on the cross- perfectly fulfilling Passover, on the very day. It was because Christ paid the ransom for all with his atoning death, that the curtain was torn, thereby giving us all- Christians - direct access to God, - so that we don't have to go through the Priests.
  The 3rd temple will be built in the tribulation but it will be the Anti-Christ there, not God. The 4th Temple will be built by Christ and all the nations of the world - Jew and Gentile will celebrate Feast of Booths/ Sukkot every year - according to Zechariah, and this is very very significant because Sukkot/ Feast of Booths is God dwelling with us, and the booths were a reminder of the temporary shelters the children had when they wandered in the dessert for 40 years.

God's visible presence as His Glory is the cloud and the brilliant glow that looked like a fire but did not consume. I think it is a spiritual glow interpreted as a physical fire. When Jesus came, he assumed the function of the temple, as per N.T.Wright. God promised His visible return to Zion, and did so when Jesus was baptized. Just as looking like a fire, God's Glory descended "as a dove", a fluttering white brilliance. The onlookers had never seen God's Glory. But it suddenly came to the Temple, Jesus. It came again to all believers on Pentecost, a bright glow settling on believer's heads which was "like a flame", but I would conclude it was God's Glory coming to who now are each temples of the Holy Spirit.

When the angel appeared to Zacharias, who executed the priests' office--he burned incense in the Temple of the Lord--the angel appeared on the right side of the altar of incense

I am Gabriel who stands in the Presence of God — Luke 1:19

Gabriel does not speak of the Holy of Holies or the Ark or Gods' Presence. Also, the Holy Spirit would not be in it when Antiochus burned a pig on the altar of the Lord as did Titus. Further, after ripping it down Hadrian burned his offering to Zeus on the altar of the Lord in the place of the Zeus Temple. He replaced Gods' Temple with the Temple to Zeus and replaced with his statue of his horse on the altar place.

I agree with the position that God did not indwell the Second Temple with His presence manifested the Second Temple as it was in the First.

Being that there was no cloud of glory associated with the dedication of the second temple, and that the ark of the covenant was long gone, there's no evidence that God indwelt the second temple. Additionally, had God indwelt the second temple, it would have meant that when Jesus, who is God incarnate, entered the temple, God would have been double present there - present twofold.

I disagree with those who say God did indwell the second temple and cite as evidence the temple veil rending in two, claiming that indicates God's departure from the second temple. The counter to this argument or reasoning goes back to Ezekiel 9 & 10, where there is no mention of, or association with the temple veil renting when God clearly departed the temple then.

Rather, taking the temple veil at it's basic purpose, we realize the veil's purpose was not to "hold God in" the holy of holies, but rather to keep man out, lest anyone who enters dies. Even the chief priest, selected once a year by lottery, had much ritual cleansing (ablution) to perform so he would not be killed by entering into God's presence with any uncleanness.

So the temple veil rending upon Jesus' uttering "It is finished" better indicates that

1. the prescribed system of going through a priest and sacrifice for the symbolic removal of sins is over

2. that a torn veil now gives all men direct access to the throne.

   Consider that we are a royal priesthood ourselves now (1 Pet 2:9) and thus we no longer need a priest for the removal of our sins. That's been accomplished by Jesus, meaning we now have one mediator also between God and men, not a priest or anyone, but the man Christ Jesus, (1 Tim 2:5) who has risen and is now seated at the right hand of God(to do what?) He also intercedes for us (Rom 8:34). Neither temple, priests nor veil are needed any longer.

   The temple veil being rent in two is like saying "the old way of doing business is over." It would be tantamount today to when a brick & mortar business gets boarded up and the sign says we've now gone online.

Consider God's words to Haggai the prophet (2:7) "Then I will fill this house with glory" says YHWH of the heavenly armies. The context is God admonishing the people for settling in their own houses but leaving His house in ruins. But when God commands them to rebuild His house he promises to fill it with glory. Perhaps this is a figurative future promise but it sure seems attached to the literal building of Zerubbabel's temple.

Gods presence was at least symbolically still in the Temple during Jesus time since the curtain ripped in two upon Jesus yielding His Spirit on the Cross.

This is huge and while explained away by many in different ways, its still a mystery in others.

No longer was Gods presence to be housed in a temple or any of the old forms. Now it was to be in the new body that is be transformed to look like the risen Jesus on earth. Those who have died and been born again with Christ in our temples of flesh!

Was God's presence still dwelling in the temple while Jesus was on Earth? The answer is NO. It left the temple in Joachim's (the father of the Virgin Mary) body just before Virgin Mary conception in the Golden Gate. Please see Ann Cathaline Emmerich visions for details.

2 Chronicles 5:13-14. The Glory of God Fills the Temple:

In unison when the trumpeters and the singers were to make themselves heard with one voice to praise and to glorify the LORD, and when they lifted up their voice accompanied by trumpets and cymbals and instruments of music, and when they praised the LORD saying,"He indeed is good for His lovingkindness is everlasting," then the house, the house of the LORD, was filled with a cloud, so that the priests could not stand to minister because of the cloud, for the glory of the LORD filled the house of God. (NASB)

Matthew 23:37-39. Lament over Jerusalem:

"Jerusalem, Jerusalem, who kills the prophets and stones those who are sent to her! How often I wanted to gather your children together, the way a hen gathers her chicks under her wings, and you were unwilling. "Behold, your house is being left to you desolate! "For I say to you, from now on you will not see Me until you say, 'BLESSED IS HE WHO COMES IN THE NAME OF THE LORD!'" (NASB)

From the scriptural context that Ezekiel declares the Temple is without God, that Jesus found it a den of thieves (Matthew 21:12-13), and from Matthew 23:38, that when Jesus left there was no presence there except when He was there, now gone.