During heart transplants does the soul remain the same or does a different soul come into the body with the new heart?

From: Vikas Dhawan

From the BG we understand that Sri Krsna said that the soul rests in the region of the heart.

 My question is that in case of a heart transplant operation the doctors remove the patients heart and transfers another heart (from a dead body, within a certain amount of time within which the heart is still living) into the body. however it has been medically observed that no trait of the person changes, so how does the soul transfer itself from one heart to another heart.