Very interesting and important question. 'Change of heart,' what is meant by that term? Change of priorities? Born again? Or what? In real-life terms, a person may be totally uninterested in spiritual things until the day, for example, he recognizes his mortality, or has a close call, and it is a wake-up call to him. His priorities change so that now he is interested in spiritual things, but he does not yet have a 'new heart' as described in the Bible, as that takes place when he dies to the old life by a conscious decision to give his life to Christ. He has not yet reached that point, but he is now open to spiritual considerations.
What do you think of that?
Well, Scripture still maintains such a person is not open to the reality of spiritual considerations (1 Cor 2:14). I've known plenty of people who are at that point of wanting more than physical reality can give, and who simply don't turn to spirituality as a reality. Spirituality is still crazy to them. (1 Cor 1:18) Someone's priorities can't change toward what he thinks is not real. (1 Cor 2:8) The endpoint of reality for someone who excludes spirituality, doesn't force the person to conclude spirituality exists.
And soul-al considerations are still the deciding issue for people who aren't spiritual. The closest I've ever seen for someone like this, is that they see some kind of soul-al benefit -- lovejoypeacepatience, something they accept as sensual pleasance -- among people who are spiritual. That doesn't make them spiritual, though. In fact it only makes them agreeable. They explain such things as futile imaginations, self-deception that they can't concur in. People don't justify the ends with the means. The means must be real, or the benefits are deceptive and suspicious.
As far as I can determine, Scripture doesn't place spirituality within someone who is unbelieving. It does place religiousness there; good works; ethics. It even places fleshly thinking within new believers (1 Cor 3:1; Rom 8:12). But it doesn't place spiritual thinking as acceptable to the soul-al person. This person does not receive things from the Spirit (1 Cor 2:14).
So what the soul-al person has at best are pipe dreams -- fond wishes for a reality they don't think exists. And that's at best.
As for a change of heart, Scripture points to changes of heart brought on by His Spirit (Rom 2:29, 2 Cor 3:3, Heb 10:16,22). I'm sure there are other responses of the heart. But I would be reluctant to expect multiple different kinds of heart changes involved with conversion, though. It seems to be an event in the New Testament. So a particular kind of heart change occurs in conversion. Other changes or even attractions of the heart do indeed occur both before and after conversion. Those will probably take time to observe, but again, I don't see them as the heart change at conversion. That would make God react not to real heart change into spiritual life -- it'd put Him responding to impulses and vicissitudes, right? I have seen much more absolute language being placed in Scripture when it comes to people's reception and reliance on Christ.