I've heard that the soul resides in the heart of each living entity. I am a cardiac surgeon. During a cardiac transplant, is the spiritual spark from one body transferred into another?

Hare Krishna! Thanks for your question. You must have many realizations in your profession!

In Srila Prabhupada's purport to Bhagavad-gita 2.17, he says:

"The influence of the atomic soul can be spread all over a particular body. According to the Mundaka Upanishad, this atomic soul is situated in the heart of every living entity, and because the measurement of the atomic soul is beyond the power of appreciation of the material scientists, some of them assert foolishly that there is no soul. The individual atomic soul is definitely there in the heart along with the Supersoul, and thus all the energies of bodily movement are emanating from this part of the body. The corpuscles, which carry the oxygen from the lungs, gather energy from the soul. When the soul passes away from this position, the activity of the blood, generating fusion, ceases. Medical science accepts the importance of the red corpuscles, but it cannot ascertain that the source of the energy is the soul. Medical science, however, does admit that the heart is the seat of all energies of the body."

The soul resides in the heart but is not bound to the heart. If you live in an apartment and your building must be torn down, you'll find another place to live. It's not that you're bound to remain there no matter what. The soul resides in the heart of the living being. If the body dies and its heart is transplanted into another body, the soul is also "transplanted," but not necessarily within the same heart. Guna (the qualities and character exhibited by that soul) and karma will determine the soul's next destination.

Another consideration is that the fact that the soul resides in the "heart" of a living entity. The "heart" in that statement is also a synonym for "core" of that person, rather than meaning the literal heart, which is a muscular organ in all vertebrates responsible for pumping blood through the blood vessels by repeated, rhythmic contractions.

When we say, "get to the heart of the matter," we mean get to the essence. So Krishna is in the center, the core, the heart of the living entity, and the essence of the body is the jiva. It is that core being around which the body is fitted and from which the energy of the entire body is emanating.

I hope this is helpful!
Your servant,
Laxmimoni dasi