First, during his initial remarks at the dedication of the temple, he says,
... the LORD said to my father David, "Since it was your desire to build a temple for My name, you have done well to have this desire. Yet you are not the one to build it; instead, your son, your own offspring, will build it for My name" (18-19 HCSB).
In the obvious sense, Solomon is the fulfillment of that prophecy (as v. 20 indicates). Solomon built the temple.
But in the ultimate sense, it could be a reference to the Son of David, Jesus.
In John 2, Jesus has an exchange with the Jews in which he says to them, "Destroy this temple, and I will raise it again in three days" (19 NIV). They think he's talking about the physical temple in which they are standing as they debate Jesus. But John makes clear that Jesus had a different temple in mind.
The Jews replied, "It has taken forty-six years to build this temple, and you are going to raise it in three days?" But the temple he had spoken of was his body (20-21, emphasis added).
The whole incident in John 2 shows that Jesus replaces the temple. Jesus becomes the new temple, the place where people meet with God.
So, yes, Solomon, David's offspring, built the first temple, but (an even bigger yes) Jesus, David's offspring, build the final ultimate temple. It is in Jesus that we come to God the Father (see John 14:6).
Second, Solomon has built a "house" for the LORD (vv. 13, 16, 17, etc.), but he recognizes that unlike a human house, the occupant of the LORD's house will not be primarily confined to it: "But will God indeed dwell on the earth? Behold, heaven and the highest heaven cannot contain you; how much less this house that I have built!" (27 ESV)
This is no quaint theological creed that Solomon slips in and out of. The fact that God does not dwell primarily in this temple is evident throughout his prayer. Throughout the various scenarios Solomon specifies in his dedicatory prayer, he peppers eight specific requests to "hear from heaven" (emphasis added), sometimes referring to heaven as "your dwelling place."
- Hear from heaven, your dwelling place, and when you hear, forgive. (30 NIV)
- ... hear from heaven and act. (32)
- ... hear from heaven and forgive the sin of your people Israel and bring them back to the land you gave to their fathers. (34)
- ... hear from heaven and forgive the sin of your servants, your people Israel. (36)
- ... hear from heaven, your dwelling place. Forgive and act ... (39)
- ... hear from heaven, your dwelling place, and do whatever the foreigner asks of you ... (43)
- ... hear from heaven their prayer and their plea, and uphold their cause. (45)
- ... from heaven, your dwelling place, hear their prayer and their plea, and uphold their cause. (49)
In a similar vein, let us understand that our Lord is not like the leaders of other religions. He is not equal to Mohammad, or to Moses (or David), or to Buddha. He is the supreme one whom everyone will worship (Rev 5:8-14; Php 2:10-11). "God exalted him to the highest place and gave him the name that is above every name" (Php 2:9 NIV, emphasis added).