There are three main elements of a temple complex in Mesopotamia: the temple itself, a ziggurat, and a garden. The garden ‘symbolized the fertility provided by the deity.’ (Walton, p. 122) So you have the ziggurat (how the deity come down to earth), the temple (where the deity dwells to bless his people and receive their worship), and the garden (the tangible form of the blessings from the deity). Furthermore, the gardens were watered from the waters that flowed from the temples. And there were four streams flowing from the temple to water the four corners of the earth, signifying a life-giving deity.
And this is reflected in Eden: ‘a river flowed out of Eden to water the garden (!), and there it divided and became four rivers.’ (Gen 2.10) So the principle is similar. Eden is the temple proper itself, where God dwells, and man lived in the garden of Eden, watered from a river that flowed out of Eden (i.e., it was God who sustains life for man).
And also in the New Jerusalem: ‘then the angel showed me the river of the water of life, bright as crystal, flowing from the throne of God and of the Lamb through the middle of the street of the city.’ (Rev 22.1-2) Why is there no temple? ‘And I saw no temple in the city, for its temple is the Lord God the Almighty and the Lamb.’ (Rev 21.22) Since the temple is to mediate the presence of God, and God himself was present, hence temple is rendered obsolete. Nevertheless, the water of life remains, but now not flowing into a garden, but into a city (which symbolized human development throughout history).
So now perhaps it is clear what does it mean when Jesus, “If anyone thirsts, let him come to me and drink. Whoever believes in me, as the Scripture has said, ‘Out of his heart will flow rivers of living water.'” (Joh 7.37-38) The water of life comes not from the temple, but from Jesus. Jesus is the very presence of God himself (and it rendered the temple obsolete in the process; the saying took place in an incident in Jerusalem, as well).