How can one distinguish between the heart and the mind, and which of them is correct when they contradict each other regarding a certain matter?

Both the heart and the mind can err or be correct. The mind may judge something, while the truth is otherwise, and the heart may incline towards something, while the truth is otherwise. Therefore, a person must connect their intellectual and psychological faculties to the infallible revelation (the Qur’an and the Sunnah), because they are the source of truth. To the extent that a person is connected to this source, in knowledge and in action, will be their attainment of truth and their ability to distinguish it from falsehood. Allah Almighty has named those who follow His Book and the Sunnah of His Messenger as "people of understanding."