The power released by magnetic nanoparticles submitted to an alternating driving field is temperature dependent owing to the variation of the fundamental magnetic properties. Therefore, the heating efficiency of magnetic nanoparticles for applications in precision nanomedicine (such as magnetic hyperthermia or heat-assisted drug delivery) can be significantly affected by the local instantaneous temperature of the host medium. A rate equation approach is used to determine the hysteretic properties and the power released by magnetite nanoparticles, and the heat transport equation is solved in a simple geometry with boundary conditions appropriate to both in-lab experiments and in vivo applications. Size plays a fundamental role in determining the heating efficiency of magnetic nanoparticles; above a critical size, nanoparticles remain inactive, although they can undergo secondary activation. The experimental conditions for optimal thermal efficiency are expressed by a thermal activity diagram for nanoparticles. In the light of the model's results, features, methods, advantages and dangers of magnetic-particle assisted precision nanomedicine ought to be reconsidered. In vivo antitumor applications should take into account the hazards arising from the heat generated by magnetic nanoparticles that diffuse into the neighboring healthy tissue.