The generation of topological magnetic vortex-domain structures in iron-oxide nanomaterials has promising applications in biomedical scenarios, such as heat generators for hyperthermia treatments. In this report we describe alternative kinds of magnetic-vortex nanoparticles, circular Fe3O4 nanodiscs (NDs), and dissect their heating properties by in-depth investigation of their shape and size, stoichiometry, orientations, and switching field "HS"behaviors, through experiments and theoretical simulation. We find that the stoichiometric NDs show better heating performance than nonstoichiometric materials because of the significant electron hopping between Fe3+ and Fe2+ ion. The higher heating efficiency (in terms of specific absorption rate, SAR) is observed only for the higher switching field regime, an effect that is associated with the parallel and perpendicular alignment of nanodiscs with respect to low and high ac magnetic field, respectively. A higher SAR of approximately 270 W/g is observed at a higher switching field (approximately 700 Oe) for NDs of diameter 770 nm, which increases by a factor of 4 at a switching field of approximately 360 Oe for NDs of diameter 200 nm. The reported results suggest that the heating efficiency in these systems can be enhanced by controlling the switching field, which is, in turn, tuned by size, shape, and orientation of circular magnetic vortex nanodiscs.