"Heaping coals of fire on someone's head" is a term which means to be almost maliciously nice.
The idea is that you are unremittingly pleasant and kind to a person who has treated you badly -- especially if the bad treatment was unjustified.
There is a three-fold effect to this action:
This approach only works if it is:
a) Consistent -- You cannot be unpleasant about the person, behind their back, or to their face when no-one else is around (although you can talk about their treatment of you in a calm, reasonable way: "I was hurt when X did so and so" etc.)
b) Genuine kindness -- Wish them a happy birthday on the right day, wish them good luck for a test, answer their questions if you are in the group asked, invite them to group social events etc.
This behaviour goes along with the phrase "The best revenge is to live well", and it is very satisfying.