Paul also made use of repentance-words in some of his letters, although the contexts tend to be somewhat more complex than those in the Gospels or in Acts. For instance, in Romans 2:4-5, Paul uses forms of metanoia twice:
4 Or do you despise the riches of his goodness, forbearance, and patience, not knowing that the goodness of God leads you to repentance (metanoian)? 5 But according to your hardness and unrepentant (ametanoēton) heart you are treasuring up for yourself wrath in the day of wrath, revelation, and of the righteous judgment of God…
Romans 2:4-5 (WEB).
Here, an understanding of the extended context is essential if Paul’s use of "repentance" and an "unrepentant heart" is to be understood. In verses 16 and 17 of the previous chapter, Paul explains that he is not ashamed of the Gospel, because it is the power of God for the salvation of everyone who believes both Jew and Gentile. The Gospel reveals the righteousness of God, of which we become a part by faith. Romans 1:18-22 then contrasts the faith by which believers live, bringing us into God’s righteousness, with the unbelief—indeed, the deliberate suppression of the truth of the Gospel—in which the unbelieving world collectively lives:
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness, 19 because that which is known of God is revealed in them, for God revealed it to them. 20 For the invisible things of him since the creation of the world are clearly seen, being perceived through the things that are made, even his everlasting power and divinity; that they may be without excuse. 21 Because, knowing God, they didn’t glorify him as God, neither gave thanks, but became vain in their reasoning, and their senseless heart was darkened. 22 Professing themselves to be wise, they became fools, 23 and traded the glory of the incorruptible God for the likeness of an image of corruptible man, and of birds, and four-footed animals, and creeping things.
Romans 1:18-23 (WEB) (emphasis added).
The point of this passage is not that God gives perfect knowledge of himself to everyone, regardless of whether they have faith, or even that God gives everyone enough knowledge of himself to be saved. Instead, Paul’s argument is that God gives some knowledge of himself, of his power and of his nature as one and only one God we should seek and obey, to everyone, and everyone, without exception, initially suppresses this knowledge. Rather than to seek and to glorify the real, but sovereign, God we know to exist, we pervert our thinking, and fill our minds with empty ("vain") thoughts of deities we can manipulate.
The end result of this process, at least in the Gentile world of Romans 1:24-32, is that God progressively gives up individuals and cultures collectively to do all kinds of evil with a "debased" or "reprobate" mind that can no longer recognize evil (except perhaps when it is done to oneself or one's friends). The acts that characterize people of "reprobate," "debased" minds sound a great deal like what is honored and promoted in our present Western culture:
…being filled with all unrighteousness, sexual immorality, wickedness, covetousness, malice; full of envy, murder, strife, deceit, evil habits, secret slanderers, 30 backbiters, hateful to God, insolent, haughty, boastful, inventors of evil things, disobedient to parents, 31 without understanding, covenant breakers, without natural affection, unforgiving, unmerciful; 32 who, knowing the ordinance of God, that those who practice such things are worthy of death, not only do the same, but also approve of those who practice them.
Romans 1:29-32 (WEB).
Of course, this list of evils would also have appeared to a good Jew like Paul to be an excellent description of First Century Hellenistic and Roman culture. (The list has a certain timeless quality). It is because of this self-righteous Jewish response to the obvious evils of the pagan Roman world that Paul wrote chapters 2 and 3 of Romans. These chapters are directed primarily at Jewish self-righteousness, but also have valid application to the judgmental, self-righteous pride of Christians and of righteous-appearing unbelievers associated with Christian churches (mere "cultural" Christians).
Paul starts his denunciation of self-righteous pride with the words "therefore you are without excuse, O man, whoever you are who judge. For in that which you judge another, you condemn yourself. For you who judge practice the same things." Romans 2:1. He goes on to explain that, when we judge others, we clearly recognize that the evils we judge are worthy of God’s judgment, since we judge it ourselves, yet we do the same things. It is at this point in his argument that Paul brings in the concept of repentance, and the metanoia words. The references to repentance in 2:4 and to an "unrepentant heart" a verse later are not directed at the pagan world. They are directed at self-righteous Jews (and Christians)!
The self-righteous judge those they perceive to be less righteous—and they are often factually one third correct about their judgment, because most of those they judge really have suppressed God’s truth and have been given over by God to their wickedness. But the judgment of the self-righteous is only one third correct. What they miss is that they have sinned themselves, and are in need of repentance, and God’s mercy. The self-righteous also overlook the fact that it is God’s patience, not bringing swift judgment on us, that leads us to repentance (2:4). God patiently works with us, seeking to turn us around to follow him rather than our own lusts and the imaginary deities we believe we can manipulate. If God were to bring swift judgment, as the self-righteous do, there would be no opportunity for repentance. There would also be no preaching of the Gospel and no work of the Holy Spirit among us, calling us to repentance. It is, indeed, God’s goodness, forbearance and patience that leads us to repentance. "Repentance" in verse 4, refers quite plainly to a change in both attitude and behavior, turning “to God from idols to serve the living and true God.” (1 Thessaonians 1:9).
This is further demonstrated by verses 5 through 9 of Romans 2. In verse 5, quoted above, the self-righteous are said to have hard and "unrepentant" hearts—"unrepentant," literally, "without repentance" (ametanoēton), because they cannot even recognize their own need for repentance. Because of their inability to discern their own need, the self-righteous are, according to verse 5, storing up wrath for the day when God finally reveals his judgment. This parallels Jesus’ warning and observation about judgment: "Don’t judge, so that you won’t be judged. For with whatever judgment you judge, you will be judged; and with whatever measure you measure, it will be measured to you." Matthew 7:1-2. Paul then goes on to discuss the basis for God’s ultimate judgment against all unbelievers—both the knowingly wicked and the self-righteous—in terms that make it quite clear that God’s judgment will be based on both their deeds and their attitude toward Him. Paul first declares that God will "pay back to everyone according to their works." (Romans 2:6), but then sets forth what those "works" are:
to those who by patience in well-doing seek for glory, honor, and incorruptibility, eternal life; 8 but to those who are self-seeking, and don’t obey the truth, but obey unrighteousness, will be wrath and indignation, 9 oppression and anguish, on every soul of man who does evil, to the Jew first, and also to the Greek. 10 But glory, honor, and peace go to every man who does good, to the Jew first, and also to the Greek. 11 For there is no partiality with God.
Those who have the right attitude toward God also "do good," and "seek for glory, honor and incorruptibility." Those who have the wrong attitude toward God, who are "self-seeking" and disobedient to the truth, also "do evil." The repentance spoken of in verse 4, thus, has a dual aspect—it involves both turning back to God from a self-seeking and idolatrous attitude, and doing good instead of the accustomed evil.
See, also,A Warning Against Idolatry.