Rom 12:19-21, 19 Beloved, never avenge yourselves, but leave it to the wrath of God, for it is written, “Vengeance is mine, I will repay, says the Lord.” 20 To the contrary, “if your enemy is hungry, feed him; if he is thirsty, give him something to drink; for by so doing you will heap burning coals on his head.” 21 Do not be overcome by evil, but overcome evil with good.
The thought in vs. 19 seems to follow from what precedes vs. 18. It may sometimes be impossible to be at peace with all; but at any rate, do not increase bitterness by avenging yourselves. Knowing the wicked has a day in court with the Lord, Paul took his own advise in dealing with one who did him great harm, 2Ti 4:14 “Alexander the coppersmith did me great harm; the Lord will repay him according to his deeds.“
The admonition is to not take matters in hand to avenge but to do good. Men in general desire vengeance on their enemies, expressed proverbially by heaping coals of fire on their head. If you have enemies, do them good. This is the only vengeance, the only coals of fire allowed of a Christian. That is, do not, “Be not overcome of evil, but overcome evil with good.” Believers are suppose to shine by being different from the way the world would want us to respond to our enemies.