I don't see the relevance. A born again believer is born of the Spirit. So, when the Bible speaks of a NEW heart, it's not talking about the blood pumping organ. If the organ needs a transplant, and one is available, replace it.
If it's a question of faith, IE, should he/she BELIEVE God for a miraculous healing, that's up to the person. We could encourage them to believe, but give them the right to say, "I don't know if my faith is that strong".