ck, Jesus leaves no doubt about how we should love God. We are to employ all aspects of our being:
Mark 12:30 And thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind, and with all thy strength: this is the first commandment.
I have come to conclude that during my atheistic years I searched because of the dissent of my heart. My mind was made up against God. I resisted the Lord with all my strength. My soul was in the balance. So I would say that seeking God with your heart means to recognize and give space to all parts of your being in your seeking. I would reckon that heart = our spirit, or our life force; that part of us that can "know" and give us "knowledge" of God.
I Samuel 3:10 And the LORD came, and stood, and called as at other times, Samuel, Samuel. Then Samuel answered, Speak; for thy servant heareth.