Ask the Virgin Mary to melt your own icy heart and for it to be changed into the likeness of Jesus' Heart.
Many saints have encouraged Christians to draw closer to the Immaculate Heart of Mary, and by so doing, be brought closer to Jesus and his Sacred Heart.
Here is a prayer from the Raccolta, asking Mary in a special way to melt our icy hearts.
O heart of Mary, mother of God, and our mother; heart most worthy of love, in which the adorable Trinity is ever well-pleased, worthy of the veneration and love of all the angels and of all men; heart most like to the Heart of Jesus, of which thou art the perfect image; heart, full of goodness, ever compassionate toward our miseries; deign to melt our icy hearts and grant that they may be wholly changed into the likeness of the Heart of Jesus, our divine Savior. Pour into them the love of thy virtues, enkindle in them that divine fire with which thou thyself dost ever burn. In thee let Holy Church find a safe shelter; protect her and be her dearest refuge, her tower of strength, impregnable against every assault of her enemies.
Be thou the way which leads to Jesus, and the channel, through which we receive all the graces needful for our salvation. Be our refuge in time of trouble, our solace in the midst of trial, our strength against temptation, our haven in persecution, our present help in every danger, and especially at the hour of death, when all hell shall let loose against us its legions to snatch away our souls, at that dread moment; that hour so full of fear, whereon our eternity depends. And then most tender virgin, make us to feel the sweetness of thy motherly heart, and the might of thine intercession with Jesus, and open to us a safe refuge in that very fountain of mercy, whence we may come to praise Him with thee in paradise, world without end. Amen.