And Moses in several places speaks of God's anger being kindled. Paul here introduces a quotation from Solomon. Prov 25, 21-22. Heaping coals of fire on the head, to my thought, implies conferring favors upon the enemy. Being enkindled by our kindness, he ultimately becomes displeased with himself and more kindly disposed to us.
Coals here are benefits, or favors.
I do not think a Christian should desire punishment to fall upon his enemy, though such explanation of the sentence is not inapt. Overcoming by force is equivalent to lending yourself to evil and wronging the enemy who wrongs you. By such a course your enemy overcomes you and you are made evil like himself. But if you overcome him with good, he will be made righteous like you.