Iron oxide colloidal nanomagnets generate heat when subjected to an alternating magnetic field. Their heating power, governed by the mechanisms of magnetic energy dissipation for single-domain particles (Brown and Néel relaxations), is highly sensitive to the crystal size, the material, and the solvent properties. This study was designed to distinguish between the contributions of Néel and Brownian mechanisms to heat generation. Anionic nanocrystals of maghemite and cobalt ferrite, differing by their magnetic anisotropy, were chemically synthesized and dispersed in an aqueous suspension by electrostatic stabilization. The particles were size-sorted by successive electrostatic phase separation steps. Parameters governing the efficiency of nanomagnets as heat mediators were varied independently; these comprised the particle size (from 5 to 16.5 nm), the solvent viscosity, magnetic anisotropy, and the magnetic field frequency and amplitude. The measured specific loss powers (SLPs) were in quantitative agreement with the results of a predictive model taking into account both Néel and Brown loss processes and the whole particle size distribution. By varying the carrier fluid viscosity, we found that Brownian friction within the carrier fluid was the main contributor to the heating power of cobalt ferrite particles. In contrast, Néel internal rotation of the magnetic moment accounted for most of the loss power of maghemite particles. Specific loss powers were varied by 3 orders of magnitude with increasing maghemite crystal size (from 4 to 1650 W/g at 700 kHz and 24.8 kA/m). This comprehensive parametric study provides the groundwork for the use of anionic colloidal nanocrystals to generate magnetically induced hyperthermia in various media, including complex systems and biological materials.