As someone who has dwelt long in the land of experiential pietism, to speak of “the heart” is code for the inner part of a person’s nature that no one can affect except God himself.  God gives a good heart allow an evil heart and there is nothing anyone can do about it.

But for the author of Hebrews, the heart is a corporate responsibility.  As he says in chapter 3:

Take care, brothers, lest there be in any of you an evil, unbelieving heart, leading you to fall away from the living God. But exhort one another every day, as long as it is called “today,” that none of you may be hardened by the deceitfulness of sin.

Likewise, I would think it is entirely up to God (and it is, in a way, but that doesn’t mean our actions aren’t instrumental to his plan) as to whether there be “an Esau” in our midst.  But that is not how the author of Hebrews thinks:

It is for discipline that you have to endure. God is treating you as sons. For what son is there whom his father does not discipline? If you are left without discipline, in which all have participated, then you are illegitimate children and not sons. Besides this, we have had earthly fathers who disciplined us and we respected them. Shall we not much more be subject to the Father of spirits and live? For they disciplined us for a short time as it seemed best to them, but he disciplines us for our good, that we may share his holiness. For the moment all discipline seems painful rather than pleasant, but later it yields the peaceful fruit of righteousness to those who have been trained by it.

Therefore lift your drooping hands and strengthen your weak knees, and make straight paths for your feet, so that what is lame may not be put out of joint but rather be healed. Strive for peace with everyone, and for the holiness without which no one will see the Lord. See to it that no one fails to obtain the grace of God; that no “root of bitterness” springs up and causes trouble, and by it many become defiled; that no one is sexually immoral or unholy like Esau, who sold his birthright for a single meal. For you know that afterward, when he desired to inherit the blessing, he was rejected, for he found no chance to repent, though he sought it with tears.

In my language-world, the only corporate exhortation that could be made about an “evil heart” or an “Esau” would be to expel such a person.  According to the author of Hebrews we are to prevent anyone from developing in this way by exhorting one another, lifting up drooping hands, and strengthening weak knees, to make sure that “no one fails to obtain the grace of God.”