“heap burning coals on his head”

This idiom originates in Proverbs and is cited once in the New Testament:

If your enemy is hungry, give him bread to eat, 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. (Proverbs 25:21-22 ESV)

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)

In the absence of any other information, it appears to mean just what it says.