It depends.
If you've been born again, you have been given a new heart that is good. Not born again? Not so much.
Here again is my diagram of the makeup of the heart. (I diagram everything.) The heart is the convergence of the desires/emotions, the mind/beliefs, and the will/intentions.
One of the more familiar verses in the Bible about the heart is Jeremiah 17:9
“The heart is deceitful above all things, And desperately wicked; Who can know it?"
What's the point of even studying about our heart if it's deceitful and wicked? Are our hearts desperately wicked? The answer is yes and no, because before you were saved you were separated from Christ and your heart WAS desperately wicked, but when you were saved, God gave you a new heart. He had promised this in Ezekiel 36:26.
"I will give you a new heart and put a new spirit within you; I will take the heart of stone out of your flesh and give you a heart of flesh."
When Jesus saved you, your spirit was joined with His. This united your heart to His heart, giving your heart new capabilities that it didn't have before. Your new heart has the capability to desire what Jesus desires, to think what Jesus thinks, and to intend what Jesus intends. So you and I have the ability (and responsibility) to choose to tune in to Jesus heart and rejecting the demands of our old wicked deceitful heart.
The desires of your old heart were selfish and shallow, but God has planted new desires in your new heart.
The thoughts of your old heart were deceived, but your mind now is illumined and you have access to the mind of Christ.
Before you were saved your will was misdirected to useless things, but your will now is empowered by the Holy Spirit.
"It is God who works in you both to will and to do His good pleasure." (Philippians 2:13)
John Eldredge in his book "The Ransomed Heart" says this: "I'm just a sinner saved by grace. I'm just clothes for God to put on. There sure isn't any good thing in me. It's so common, this mind- set, this idea that we are no-good wretches, ready to sin at a moment's notice, incapable of goodness...yes, we still battle with sin... We have to choose to live from the new heart, and our old nature doesn't go down without a fight...Does the Bible teach that Christians are nothing but sinners - that there is nothing good in us? The answer is no! Christ lives in you. You have a new heart. Your heart is good. That sinful nature you battle is not who you are."
This is how I define the flesh: that old left over heart that's still around as long as we're in these bodies. We still have the option of choosing to operate out of that old heart, out of the flesh even though it's been crucified with Christ and it's not who we are anymore. What we have to learn to do is to count that old heart as dead and choose to operate out of the new heart that is united with Jesus' heart.
So from this point on we're proceeding with the knowledge that you are a new creation, your heart is united together with Jesus' heart, and your goal is to draw from the desires, the knowledge, and the will of this new heart.