In the scruipture it is a metaphore. "Heart" is metaphore for predisposition. You read it metaphorically as well, as you surely don't think that something physiologically changed in the Pharaoh's heart muscle. Yes, God played exactly the role the Scripture describes: He hardened Pharaoh's heart as well as Pharaoh hardened his own heart, and after that change of heart the Pharaoh persecuted Moses and his people. God predisposed and the Pharaoh disposed, in the way contrary to the will of God.
If God predisposed the heart of Pharaoh, isn't that the same as God specifically directing the heart to follow one path? Couldn't God have predisposed Adam's heart to take the fruit?