This is the point of the famous Sermon on the Mount. Jesus first says we haven't a hope of heaven unless our righteousness "surpasses that of the Pharisees" (Matt. ). How can that be? They were fastidious rule keepers, pillars of the church, model citizens. Yes, Jesus says, and most of it was hypocrisy. The Pharisees prayed to impress men with their spirituality. They gave to impress men with their generosity. Their actions looked good, but their motives were not. Their hearts, as the saying goes, weren't in the right place. A person's character is determined by his motives, and motive is always a matter of the heart. This is what Scripture means when it says that man looks at the outward appearance, but God looks at the heart. God doesn't judge us by our looks or our intelligence; he judges us by our hearts.
It makes sense, then, that Scripture also locates our conscience in our hearts. Paul says that even those who do not know God's law "show that the requirements of the law are written on their hearts, their consciences also bearing witness" (Rom. 2:15), such as when your child looks guilty for having told a lie. This is why it is so dangerous to harden our hearts by silencing our consciences, and why the offer of forgiveness is such good news, to have our "hearts sprinkled clean from an evil conscience" (Heb.10:22 NRSV). Oh, the joy of living from right motives, from a clean heart. I doubt that those who want to dismiss the heart want to dismiss our consciences, set aside the importance of character.