I've been doing some reading about "drawing the mind into the heart"
No, it is actually quite literal. Let me explain. In my experience the prayers that are that are clearly answered always involve the heart in some way. And sometimes when I pray I am especially aware of my awareness moving inward or downward, to a less intellectual point of view but one that is more intuitive or emotional.
I used to practice yoga and the idea of the heart being a center of consciousness or connection to God is not strange at all in Asian cultures. In fact I still see alot of benefit in yoga but it's not necessarily working on the same spiritual level as Jesus Christ... it's just a tool, not a substitute.