Romans 12:19 forbids Christians from taking revenge. Romans 12:20 give us the replacement action when tempted to take revenge.
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.”Romans 12:20 (ESV)
Jesus taught the same in Matt 5:43-48, but this is a direct quote of what the wise believers in the Old Testament practised:
If your enemy is hungry, give him bread to eat,Proverbs 25:21-22 (ESV)
and if he is thirsty, give him water to drink,
for you will heap burning coals on his head,
and the LORD will reward you.
There is a reward from God Himself to all who do not take their own revenge, but rather repay the evil done to them with deeds of practical kindness instead.
The idiom of “heap burning coals on his head” is not a reference to burning a person for what they’ve done to you. Quite the contrary. It refers to the way in which a hard surface was softened. Like a blacksmith would soften even thick cold metal by placing burning coals on it, so an act of Christian kindness softens the heart of even the worst of enemies.
Another way of phrasing this idiom would be to say “If you enemy is hungry, feed him, for you will make him blush red-hot for how he treated you, and the LORD will reward you.”
When your enemy needs something from you, give it freely. This is something that innocent children often practise more willingly than adults. Remember the girl in 2 Kings 5 and what she did for the man who destroyed her home, tore her from her family, and then forced her into slavery. If a little girl with faith in God can do it, so can you and I.