The heart has always been associated with emotions, especially love, excitement and fear, probably because when we feel a strong emotion we feel our heart thumping and beating faster. So when something "warms the cockles of our heart", it is a reference to something pleasant that makes our heart beat faster and makes us feel good. It is probably also the origin of the saying that something gives us that "warm and fuzzy feeling".
John Frith, Paddington
The cockles of the heart are its ventricles, named by some in Latin as "cochleae cordis", from "cochlea" (snail), alluding to their shape. The saying means to warm and gratify one's deepest feelings.
