Not to get too far afield, and though Matthew is not to be interpreted by John, it is little wonder then, that the Gospel of John, in its portrayal of Jesus that reflected the development of Christian understanding about Jesus and a better grasp (in the late first century in the time period after the fall of the Temple) of Jesus’ sayings about Himself, has Jesus telling Nathanael and the other men that had been called to be His disciples, that they “will see heavens opened and the angels of God ascending and descending upon the Son of Man” (John 1:51b).
Yes, the early church clearly understood that Jesus was the true Temple. He Himself was understood to be the house of Israel’s God. He was the place where heaven and earth came together. By the gifting of His Spirit (or as the evidence of the presence of the Spirit of the Creator God), His church would carry out His mission as the Temple, thus becoming the extension of His own faithfulness.
Naturally, if talk about the church as the Temple of the Holy Spirit is taken seriously (as can be seen in the pre-Matthean letters of the Apostle Paul, though Paul would have drawn from the Jesus traditions that would eventually come to be concretized by Matthew and the other Gospel writers, while also having a hand in the theological shaping of those Jesus-centered narratives) in both a communal sense and in accord with the responsibility of the individuals members that compose the body of the Christ, this realization about the role of the church as the Temple (the place where heaven and earth are to come together) informs the Christian as to his or her responsibilities in association with a life lived in response to the Gospel claim that Jesus is Lord.
Yes, the Christian is to be the place where and heaven earth come together---bringing heaven to earth as a singular purpose (and this will look a lot like caring for orphans and widows, which is the constant cry of the prophets of the Hebrew Scriptures). The church, as the collection of individual elected ones (Christians), carries out this purpose in community.
This brings this study back to Matthew sixteen and Jesus’ statement to Peter. Having established that the Temple was the concrete and understood point of reference with talk of earth and heaven (throughout the New Testament and demonstrably so in Matthew and all of the Gospels), while also establishing that Jesus sees Himself as the new Temple, a great hermeneutical service has been provided. By extension then, continuing with said hermeneutic, and doing so in line with the earliest interpreters of the Jesus’ tradition, the church (and its members), as it (and they) carries out the mission of Jesus and as it (and they) is infused with the same Spirit by which Jesus was raised up from the dead, is to be conceived of as the Temple in so far as it represents Jesus in, to, and for the world.
Therefore, talk of earth and heaven, within an appropriate context, becomes talk of the church. This knowledge can be employed and deployed when hearing Jesus speak to Peter. Peter has just insisted that Jesus is “the Christ, the Son of the living God” (16:16b). Part of Jesus’ response to this declaration is to tell Peter that “flesh and blood did not reveal this to you, but My Father in heaven!” (16:17b) The use of flesh and blood presents an unspoken contrast of revelation by a means other than flesh and blood. When Jesus says “My Father in heaven” revealed this to Peter, having set “flesh and blood” in juxtaposition, He is making an obvious reference to the activity of the Creator God, by means of His Spirit.