A more common condition is atherosclerosis, better known as hardening of the arteries. It is caused by deposits of fatty material, such as cholesterol, in the blood vessels. Unlike many other sclerotic conditions, there are not outward symptoms until the arteries are really in bad shape and the blood can barely get through.
Jesus describes what we might call spiritual sclerosis in Matthew 13:15. He quotes Isaiah 6:9 and applies it to the multitudes of His time. He says, For the hearts of this people have grown dull [which could mean fat or calloused]. Their ears are hard of hearing, and their eyes they have closed . . .. Their hearts, well as their other senses, had become insensitive so they were unable to receive what Christ was saying to them.
That's what the author of Hebrews is warning against - a gradual hardening of the heart, a sclerosis, that causes spiritual impairment that will ultimately be fatal because the word of God no longer has any effect.
Now, the hardening of the heart does not have to do with human feelings. That is, the author is not warning against becoming sociopaths, devoid of empathy. One can be good-natured, warm, kind, and forgiving on a human level and yet still be hard-hearted in spiritual matters.
This phrase is not talking about one's disposition toward other people, but instead whether one is disposed to hear God and respond. Of course, if one truly is responding to God, then there is a much greater chance that one's other relationships will be good as well. But being sensitive to others is not always a good gauge of one's sensitivity to the things of God.
In hardening of the arteries, the danger stems from the accumulation of stuff that doesn't belong, and which makes the arteries less able to circulate our life-sustaining blood, and thus, less effective. So, the danger is one of gradualism. It happens slowly and without symptoms until suddenly you have chest pain and shortness of breath. It doesn't develop from a single helping of French fries. But if you're eating a doughnut, oozing the trans-fat, three times a day, there's going to be a problem. That's just how it works - it's natural law. The deposits and the hardening develop over time through what is taken in on a regular basis. And this applies spiritually as much as it does physically, and the ramifications are far more serious.
What we put in our minds on a regular basis accumulates and can cause sclerosis where God is concerned. Spiritual sclerosis is a heart that is clogged with ideas, priorities and habits that make it harder to run our race because our spiritual capabilities have degraded.