Calvin does use the word “heart” in many ways throughout The Institutes. But at least when he’s talking about the depravity of the psychological faculties, he takes the biblical uses of “heart” as references to the corrupt will. I think this is a problem, but I make no comment about that here. But to preserve a key example:
God, therefore, begins the good work in us by exciting in our hearts a desire, a love, and a study of righteousness, or (to speak more correctly) by turning, training, and guiding our hearts unto righteousness; and he completes this good work by confirming us unto perseverance. But lest any one should cavil that the good work thus begun by the Lord consists in aiding the will, which is in itself weak, the Spirit elsewhere declares what the will, when left to itself, is able to do. His words are, “A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh. And I will put my Spirit within you, and cause you to walk in my statutes, and ye shall keep my judgments, and do them,” (Ezek. 36:26, 27). How can it be said that the weakness of the human will is aided so as to enable it to aspire effectually to the choice of good, when the fact is, that it must be wholly transformed and renovated?
John Calvin, Institutes, II.3.6