From the article Luther on Free Will:
Commenting on Pharaoh’s heart being hardened by God, Luther wrote: “His [Pharaoh’s] evil will would not have been moved or hardened of itself, but as the omnipotent Agent makes it act (as he does the rest of his creation) by means of his own inescapable movement” (207). God did not merely “permit” Pharaoh’s heart to be hardened of itself. God “makes it act by means of his own inescapable will.” Furthermore, God did not simply look into the future and see what Pharaoh would do. God is the one who actually caused the hardening of his heart. On God’s foreknowledge, Luther wrote: “Had there been in Pharaoh any power to turn, or freedom of will that might have gone either way, God could not with such certainty have foretold his hardening” (211).
There are plenty of passages in the Bible were people make other people do things. In the example cited, Pharaoh’s heart is actually hardened in several passages by various actors:
Exo 7:3 And I will harden Pharaoh’s heart, and multiply My signs and My wonders in the land of Egypt.
Exo 7:13 And Pharaoh’s heart grew hard, and he did not heed them, as the LORD had said.
Exo 8:15 But when Pharaoh saw that there was relief, he hardened his heart and did not heed them, as the LORD had said.
Exo 7:22 Then the magicians of Egypt did so with their enchantments; and Pharaoh’s heart grew hard, and he did not heed them, as the LORD had said.
The last passage is interesting. The wording suggests that God’s statement was predictive more than a statement that God was magically hardening Pharaoh’s heart. This understanding is well in line with normal modes of speech. Other people in the Bible are said to “make” third parties do things. For example, Jeroboam makes Israel sin:
1Ki 22:52 He did what was evil in the sight of the LORD and walked in the way of his father and in the way of his mother and in the way of Jeroboam the son of Nebat, who made Israel to sin.
The idea is not that Jeroboam is magic. Instead the idea is that the people willingly followed Jeroboam’s leadership. This was not a violation of free will, as much as a willing following of a leader. Much in the same way, the Exodus account reads as if God is predicting rather than overriding Pharaoh’s will:
Exo 3:19 But I know that the king of Egypt will not let you go unless compelled by a mighty hand.
The text shows God finding an opportunity to use Egypt as an object lesson. It is reading too far into the text to see this has God overriding someone’s free will. That is counter to specific wordings in the passage and discounts what we know about normal standards of communication.
I wish I had written my long explanation of the hardening of Pharaoh’s heart in English. I believe God did sometimes override pharaoh’s will. This is not in contradiction with several biblical Open Theists.