I began trying to live by heart-thinking a good while before I became a Christian - but I found that it provided only a negative form of guidance - as in This Poem - by Robert Graves.
In other words, my heart would tell me when I was on a wrong path, had made an error - by the psychological consequences of meaninglessness, alienation, disenchantment... I would know I needed to get off the current track, and find a different way of living.
Different - yes; but how?
But it was no use at all in deciding what I ought to be doing - what my purpose should be - because, as a non-Christian, a non-theist, I did not acknowledge any purpose to reality, nor to my life. Or, that is; my purpose reduced to attending to my current psychological well-being.
That is the kind of partial (and unsatisfactory) insight into the need for primacy of intuition of, say, New Age, Neo-paganism, Jungianism and the like. That is; Non-Christian (or anti-Christian) romanticism - in general - of which Robert Graves was an exemplar.
Therapy is as far as this can take us.
Only after becoming a Christian, and indeed a Romantic Christian, was I able to see why and how the thinking of the heart could be a guide to the future.
In other words, for heart-thinking genuinely and fully to replace intellect as the primary (not the only) way of thinking requires Romantic Christianity.