Heart disease affects many people and heart transplants are becoming more common. Limited shelf life is a major hindrance to the success of heart transplants. Cryopreservation opens an avenue for increasing shelf life. Our goal in this study was to model the preservation of a heart using finite element software to determine the time needed to sufficiently cool the heart and to compare the average temperature to the maximum temperature of the heart. We found a range of minimum times varying with material properties of the heart. We concluded that computer simulation can be used to approximate the minimum time needed to reach a desired maximum temperature. We also found that average temperature of the heart during cooling was not an accurate approximation of the maximum temperature.