Chapters 1-6 are in response to the issues that Chloe raised and chapters 7-16 are in response to the issues raised in the letter carried by those three leaders.
But back in 2010, Ciampa and Rosner wrote a commentary1 that many people are now referring to as having demonstrated quite well that unity is only one of the sub-themes in the book and that Paul weaves every argument through the lens of the church being God's new temple to show forth God's glory.2 Paul brilliantly uses Deuteronomy, Isaiah, and Malachi to show how the purpose of God's grace was to save people from their sins, to purify them and to make them ready to meet in the presence of God's glory as a unified people. The glory of God in His temple is the central theme that ties every sub-theme together - the glory of God in His temple.

4. Even the four major themes of "the lordship of Christ, worldwide worship, the eschatological temple, and the glory of God" are rooted in the Old Testament. p. 33. Here is a sample quote of how they seamlessly tie these themes together: "The expression echoes Malachi 1:11 LXX,111 which (in a context of frustration over the way the Lord is being worshiped in Jerusalem) prophesies a future time when God would be worshiped by Gentiles “in every place”: “From the rising of the sun until its setting my name will be glorified among the Gentiles, and in every place incense is offered to my name and a pure offering, for my name is great among the Gentiles, says the Lord Almighty.” Similarly, Haggai 2:7 anticipates a time when the Gentiles will glorify God in his temple: “all nations will come in, and I will fill this house with glory, says the LORD of hosts.” The echo of Malachi 1:11 in 1 Corinthians 1:2 suggests that the Corinthians are part of the fulfillment of God’s plan to be worshiped among all the Gentiles and that it is Paul’s ultimate purpose in writing to them to see them play their part in fulfilling this world-wide eschatological vision by glorifying God (see 6:20b and 10:31b)." p. 34. ↩
   The word "sanctified" or "holy" was used to describe Israel as a holy people. The closer to God's temple something was in the Old Testament, the more holy it was. But he will point out that an outwardly holy people can be inwardly defiled just as Israel was.

To "call on the name" is an Old Testament expression connected with the temple, but when he says that they together with the broader church are gathered to do so, he implies that Corinth must have a unity with all the churches if they are to meet God's purpose as a temple. It's not the local church that is God's temple, but the entire church meeting before God's throne. It gives you a different perspective than basing everying on the local church.

But the most pointed reference in verse 2 is the quote from Malachi 1:11. Malachi dealt with the division, immorality, and dishonor that was happening at the postexilic temple - the same kind of issues that Corinth was going through. And Malachi prophesied that in the New Covenant that would eventually change: "from the rising of the sun, even to its going down, My name shall be great among the Gentiles; in every place incense shall be offered to My name, and a pure offering; for My name shall be great among the nations." The offering up of incense in every place was a reference to the universal church offering up prayers in every place of the world. So Paul is already setting up a Messianic temple context and hinting that Corinth is not living in light of this paradigm. Otherwise, why appeal to Malachi?

Paul pronounces grace and peace upon them in verse 3, and shows that those two can only come from heaven. Corinth desperately needs peace, but before they can have peace, they must receive grace. There is an order to those terms that cannot be reversed. And Jesus as both Lord and Messiah also sets this in the context of Malachi's New Covenant temple.

But look at the praise in verses 4-9. I find it remarkable that this epistle is so filled with praise. They were a messed up church and he had to correct a lot of things, but he still managed to see the good and to maintain a positive attitude. To me this is remarkable. Though they had slandered him and put him down, he does not respond in kind. We would do well to do the same. When you are offended, take the high road. I was going to preach on these verses,6 but for sake of time will just read them:

Even the resurrection chapter (chapter 15) ties in with Christ's body being the temple of God, and those who are united with Christ in His death and resurrection being a part of that temple. In fact, he says that our very bodies must properly reflect God's glory and be treated in a way that is consistent with them being part of the temple of the Holy Spirit. As Paul words it, "do you not know that your body is the temple of the Holy Spirit who is in you, whom you have from God, and you are not your own?"

It's impossible in one sermon to highlight the many ways that Paul weaves His answers to the troubles of Corinth around the theme of the glory of God's temple, but Ciampa and Rosner have made major contributions to the studies of 1 Corinthians.4 And others are building on those insights and making them more consistent - I think their book needed to be perfected. These commentaries show how every single theme of this new temple is focused on and explained by Christ - the Lord who sits on the throne of the temple. Likewise, Paul rejects the wisdom and culture of the world and seeks to show how the Messiah of the prophesied temple will replace all pagan cultures with a culture built entirely upon God's grace and His Word and in subjection to His throne.5 So there is competition between the cultures that flow from the pagan temples and the unified culture that flows from God's temple. So even the culture around the temple is to be transformed. Paul even ties his discussion of tongues (believe it or not) in with Isaiah 28, a passage that deals with God's destruction of the Old Temple and Israel (because of its defilement) and His prophecy of a new temple. Well, that's got an ominous tone to it on what could happen to Corinth if they do not repent.

And I'll just give you some examples of this theme since older books don't deal with this unifying theme very well. The whole of chapter 3 deals with God building a temple on the foundation of Christ. It is similar imagery to Ephesians 4. And his exhortation is, "Do you not know that you are the temple of God and that the Spirit of God dwells in you [plural]? If anyone defiles the temple of God, God will destroy him. For the temple of God is holy, which temple you [plural] are." (3:16-17) You divide and fight against the church? Then God will fight against you. He is jealous over His temple. If you destroy the church as God's temple, then God will destroy you. And that's a verse we can claim if persecutors try to destroy the church in America as a result of the Supreme Court decision - a decision that is inviting the LGBTQ+ crowd to come after Christians. Read Alito's opinion and you will see that this is indeed a possibility. Though he didn't write a commentary on 1 Corinthians, Meredith Kline's book, Images of the Spirit, does show how this verse is an explicit reference to the glory cloud imagery of the Old Testament.

And since the glory cloud was such a central aspect of the Old Testament temple, it is no surprise to see God's glory cloud and other aspects of God's glory being woven skillfully throughout 1 and 2 Corinthians. Christ is the Lord of glory and the Spirit is the glory of Christ inhabiting the temple.