One of the problems with cryopreserving large organs, such as the kidney is the problem of cracking. When a solid piece of matter is cooled it shrinks, and when it's warmed it expands.
Different materials shrink and expand at different rates.
In addition, its often difficult to cool or warm large bodies of matter uniformly. When cooling a kidney for example, the interior of the kidney will cool at a much slower rate than the exterior of the kidney. As a result mechanical stresses develop which can turn into cracks. While thermal expansion and contraction is a problem in organ cryopreservation, it has a number of uses. For example, if the metal lid of a jar become stuck, try running hot water over the lid.