This study explores thermal design aspects of nanowarming-assisted recovery of the heart from indefinite cryogenic storage, where nanowarming is the volumetric heating effect of ferromagnetic nanoparticles excited by a radio frequency electromagnet field. This study uses computational means while focusing on the human heart and the rat heart models. The underlying nanoparticle loading characteristics are adapted from a recent, proof-of-concept experimental study. While uniformly distributed nanoparticles can lead to uniform rewarming, and thereby minimize adverse effects associated with ice crystallization and thermomechanical stress, the combined effects of heart anatomy and nanoparticle loading limitations present practical challenges which this study comes to address. Results of this study demonstrate that under such combined effects, nonuniform nanoparticles warming may lead to a subcritical rewarming rate in some parts of the domain, excessive heating in others, and increased exposure potential to cryoprotective agents (CPAs) toxicity. Nonetheless, the results of this study also demonstrate that computerized planning of the cryopreservation protocol and container design can help mitigate the associated adverse effects, with examples relating to adjusting the CPA and/or nanoparticle concentration, and selecting heart container geometry, and size. In conclusion, nanowarming may provide superior conditions for organ recovery from cryogenic storage under carefully selected conditions, which comes with an elevated complexity of protocol planning and optimization.