Ezekiel and Hebrews show that as part of the New Covenant, Israel will have new hearts, and God will write his laws on their minds and hearts.
Ezekiel 36:24-28; Hebrews 8:10; Hebrews 10:16;
However, the New Testament, and the book of Hebrews are full of exhortations to deal with the heart.
Hebrews 3:12; Hebrews 10:22-23; Hebrews 13:9
If you have a new heart, you would not be capable of committing adultery in your heart. Have you done that lately? Matthew 5:27-28
Have you ever found obscene or hateful words coming out of your mouth when you are angry or upset? If so, they come from the heart when the mind/heart is set on the flesh. Matthew 15:17-20; Matthew 12:34-35
No spiritual growth would be required if you had a new heart and always kept his ways. 1 Thessalonians 3:11-13
Hearts and minds are used interchangeably in the Bible. If we are told by Paul that we need to be transformed by the renewing of our minds, this shows we do not have a new heart, but rather we have a heart that can be defiled or washed by the water of the word and sprinkled with Christ’s blood. Romans 12:2; Romans 8:2-7
The New Testament Epistles have many admonitions for us to deal with our heart and defilement of the flesh but the provision of the New Covenant makes it clear that this will not be an issue for the mortal Israelites who God brings back into the land to inherit the Kingdom when He comes.
Beyond the scope of what I can address here: As the Church, our spirit has been made alive together with Christ (Rom 8:10), and Christ is said to be making His home in our heart through faith as we grow in the knowledge of Him (Ephesians 3:16-21).