"This Heart of Mine" is a 1944 song written by composer Harry Warren and lyricist Arthur Freed, and featured in the musical score of the film, Ziegfeld Follies.
In the same film, Esther Williams performs a water ballet to a softer, instrumental version of the song.
Astaire plays a con artist hoping to steal some jewelry.
It concludes with the end of the ball and Astaire stealing Lucille's bracelet while kissing her.
They separate and Astaire ponders if he'd allowed his chance for real love to get away.