“For this is the covenant that I will make with the house of Israel after those days, says the LORD: I will put My laws in their mind and write them on their hearts; and I will be their God, and they shall be My people.” (Heb 8:10)
What did the apostles and patriarchs understand when they talked of things written on the heart?
“(for not the hearers of the law are just in the sight of God, but the doers of the law will be justified; 14 for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves, 15 who show the work of the law written in their hearts, their conscience also bearing witness, and between themselves)“ (Rom 2:13-15)
When gentiles did things according to ‘the law’, even though they didn’t necessarily understand ‘the law’, they showed that they had ‘the law’ in their hearts. That is, they obeyed ‘the law’ or at least parts of it even though they weren’t taught ‘the law’ as such. But because they conducted themselves according to ‘the law’ it showed that standard was written in their heart.
So according to this example of Paul, if one has something written on their heart it means that they conduct themselves in accordance with that something without even thinking about it.
“Let not mercy and truth forsake you; Bind them around your neck, Write them on the tablet of your heart” (Pr 3:3)
Solomon, here in Proverbs, encourages his son to seek and be merciful and truthful. To accomplish this He encourages his son to ‘write them, on…your heart‘. So Solomon expects that if his son has these principles written on his heart, his son will always conduct himself in accord with mercy and truth. Again a principle written on the heart causes one to act in accordance with that principle.
“Then my God put it into my heart to gather the nobles, the rulers, and the people, that they might be registered by genealogy. And I found a register of the genealogy of those who had come up in the first return and found written in it:” (Ne 7:5)
Nehemiah found it in his heart to register the returning Israelites. So he registered the returning Israelites. He did what was in his heart, not in some figurative way, but literally, in bodily fact.
“He answered and said to them, “Well did Isaiah prophesy of you hypocrites, as it is written: ‘This people honors Me with their lips, But their heart is far from Me” (Mk 7:6)
One can speak wonderful words and sayings. One can praise and glorify God, but conduct themselves contrary to their creator and worship in vain. (Mat 15:9)
“And these words which I command you today shall be in your heart” (Deu 6:6)
It is quite apparent the creator wanted them to obey. He tried them so He could tell what was in their heart. He wanted to know what they would do.
“O that there were such an heart in them, that they would fear me, and keep all my commandments always, that it might be well with them, and with their children for ever!” (Deu 5:29)
“And you shall remember that the LORD your God led you all the way these forty years in the wilderness, to humble you and test you, to know what was in your heart, whether you would keep His commandments or not.” (Deu 8:2)
“For the word of God is quick, and powerful, and sharper than any two-edged sword, piercing even to the dividing asunder of soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart.” (Heb 4:12)
In scripture, the heart is often metaphorically used to represent the mind and mindset. Our thoughts and intents are the drivers behind our actions. They hold our approach to life, one another, and our Creator. A kind-hearted person is a kind person. Not primarily because he thinks kind thoughts, but because he does kind deeds. This is not difficult to understand. The apostles, patriarchs, and our Creator took the analogy one step farther. They encouraged Israel to write His code of conduct on their heart so they would never forget and always do it.
Our Creator is faithful to the extent He will not give up on us until we understand. Some have difficulty discerning the significance of the distinction between the Sinai covenant and the Old covenant. When we have His law written on our heart we will understand and be conducting ourselves in total accord with His law and HIs way. The judgments help explain details of His Covenant, His Law.