I heard something quite similar awhile back which I always liked. Families in smaller villages, or perhaps just communities, would take turns getting up early and starting a fire for cooking and heating water throughout the day. One of the children in the family would carry some of the burning 'coals' to the other houses so that they could start their fires easily. So to me this saying was something like when you do something nice for one person, many more will benefit from it.
I like the reference to the coal on the lips too. Much to ruminate upon.
I read somewhere, don't remember where, but that heaping coals on the head, was a gesture of kindness, because some folks did not have fire(coals) to cook with and by giving the coals was just as giving food or water Like the adage rather than give a person a fish teach the person how to fish.
Don't mean to muddle the posters gathered benefit.

Heaping coals on the head :o) Another perspective is this. The coals are living stones gathered together within the wheels beneath the living creatures. The lightning flashing back and forth between them is the LIVING WORD- rhema fo God. (Exhort one another while it is still called "TODAY" to love and good works). Isaiahs "lips" were made clean and his iniquity forgiven because the "coal" of the prophetic word touched them- his speech was no longer his own. "You are all clean because of the word that i have spoken to you"- Jesus.
When we bless those who curse us and pray for those who despitefully use us we are showing forth the "lifting up" of jesus till he comes. The words that fell from His lips in the moment He was "lifted up" were, "Father forgive thenm they don't know what they are doing". When we feed our enemies, dress the wounds of our persecutors- returning kindness for injury and blessing for insult, we heap "coals of living word" upon them- opening their minds to the goodness of God and the truth of our gospel.
"If anyone receives not our gospel it is because the god of this world has blinded their eyes that they might not see the light of the knowledge of THE GLORY OF GOD IN THE FACE OF JESUS CHRIST"(2 cor 4)
When the veil is torn the light shines through. As we fill up in our bodies the sufferings of Jesus Chrsist, He is lifted up in us, we are lifted up into the heavenly realms in Christ Jesus, the "living word" touches our lips and we become ministers of reconciliation.
Woe unto me, for I am a man of unclean lips and I dwell among a people of unclean lips and my eyes have seen the Lord of glory.
Lo (behold, understand, see) this coal has touch your lips and your sin is forgiven
"Who will go for me".....
I will go for you. "Here I am(acceptable offering Ro 12 broken and contrite heart Psalm 51). Send me(releasing ones own life, dreams, goals to the will of God)."
If anyone would be my disciple let them pick up their cross and Come, Follow Me.
"Take my yoke upon you and learn of me for I am meek and lowly of heart and you will find rest for your souls."