"I will give them an undivided heart and put a new spirit in them; I will remove from them their heart of stone and give them a heart of flesh." (Ezekiel 11:19)
The prophet is promising the exiles in Babylon that they will be restored by God.
A few chapters later, Ezekiel pleads: "Rid yourselves of all the offenses you have committed, and get a new heart and a new spirit. Why will you die, O house of Israel?" (Ezekiel 18:31)
Towards the end of the prophetic book, he reiterates God's message: "I will give you a new heart and put a new spirit in you; I will remove from you your heart of stone and give you a heart of flesh." (Ezekiel 36:26)
In a similar vein, the prophet Jeremiah had predicted "This is the covenant I will make with the house of Israel after that time," declares the LORD. "I will put my law in their minds and write it on their hearts. I will be their God, and they will be my people." (Jeremiah 31:33), a passage quoted twice by the writer of Hebrews and applied to God's people under the New Covenant.
The imagery of these "new heart" passages is striking. For one thing, they provide the clearest demonstration that regeneration is completely a work of God anywhere in Scripture. Can a human being create a heart? Best we can hope for is a synthetic valve. Even then, the materials came from elsewhere. How about "I will put...I will write..." (emphasis mine). God is clearly doing the creative work here, as well as the "transplant" of the regenerate heart. This is what the New Birth is all about - His creative power redeeming what was dead. Just as we can't conceive ourselves, it's ludicrous to assume we can acquire a new heart on our own.
But pursue the analogy with me for a moment. It's not easy to be a transplant recipient. The patient has to take his or her medication, live a clean lifestyle, (smoking and drinking are out), be well-rested, and have a tissue match. At the risk of pushing the analogy too far, God expects us to take our "medicine" and be well fed - by His Word. If we aren't reading it, how do we know the implications of the new birth? He expects us to live a clean lifestyle and keep ourselves undefiled by worldliness.
After a transplant, the recipient needs to stay in isolation for a while while the body adjusts to the new organ. There is always the risk of organ rejection, which fortunately is never a spiritual concern for the new Christian! He Who has saved us is faithful to keep us from falling (Jude 1:24), but naturally as a new believer one is more vulnerable (both to temptation and error) than a seasoned believer. Being in fellowship, study, and most importantly prayer is critical to building up one's "spiritual immunity" and growing in holiness.
Sometimes, though, I find my "new heart" still thinks it's an "old heart" and wants to revert back to it's toxic ways. In so doing, it's as if I forget the Maker has done a complete and irreversible transplant. The old nature wars against and wants to instill the same deadly disease in my new heart, but God has declared me a new creation, one "born from above". It is hard to reconcile this spiritual truth with the day-to-day ugly reality of sin, but it is true.
I guess that is the whole point of conviction: to keep our consciences/hearts tender to what God would mold us into. Matthew Henry writes:
It is promised, that God will give them one heart; a heart firmly fixed for God, and not wavering. All who are made holy have a new spirit, a new temper and dispositions; they act from new principles, walk by new rules, and aim at new ends. A new name, or a new face, will not serve without a new spirit. If any man be in Christ, he is a new creature. The carnal heart, like a stone, cannot be made to feel. Men live among the dead and dying, and are neither concerned nor humbled. He will make their hearts tender and fit to receive impressions: this is God's work, it is his gift by promise; and a wonderful and happy change is wrought by it, from death to life. Their practices shall be agreeable to those principles. These two must and will go together. When the sinner feels his need of these blessings, let him present the promises as prayers in the name of Christ, they will be performed.
Have you had a "heart transplant"? You never stop needing daily consults with the Great Physician. He has indeed created in us a pure heart (Psalm 51:10), but we tend to play in the mud a lot. The born-again spirit is never going to stay clean on it's own merits, but will always seek purification through Christ, the only Mediator.