Many depictions of the Sacred Heart show flames coming from the top of Jesus' heart. This type of symbolism was not used in the Church until the 17th century, when St. Margaret Mary Alacoque had a private revelation of Jesus.
She wrote down the words Jesus told her and he specifically mentions "flames" coming from his heart.
Biblical connections
The idea of God being associated with a "fire" is also very biblical. God himself revealed his "name" to Moses in the midst of a "burning bush."
God also "preceded them, in the daytime by means of a column of cloud to show them the way, and at night by means of a column of fire to give them light." (Exodus 13:21)
Jesus used fire to communicate his desire to spread his love to all humanity.
Even the Holy Spirit appeared at Pentecost as "tongues of fire" (Acts 2:3).
While it may seem strange to see the Sacred Heart of Jesus on fire, it is a symbol that has biblical connections in addition to its origin from the private revelations of St. Margaret Mary Alacoque.