In Tolkien's earlier work The Fall of Gondolin, the Scarlet Heart was the heart of Finwë, then Turgon's father, cut out by orcs in the Battle of Unnumbered Tears. It was regained by Turgon, and made the emblem of his House.
If this story survived to be Tolkien's "final intent", then the heart would probably be that of Fingon, Turgon's brother. Finwë was slain by Morgoth himself in Aman, Fingolfin's body was taken away by Thorondor before Morgoth could desecrate it, and Fëanor's body turned to ashes after death. But altogether it is doubtful that Tolkien ever kept this story, but changed or abandoned it with much of the other material found in the Fall.