The collective organization of magnetic nanoparticles (MNPs) influences significantly their hyperthermic properties, relevant for their in vitro and in vivo applications. We report a systematic investigation of the effects of the concentration and the static bias direct current (DC) magnetic field superposed over the alternating magnetic field (AMF), both in a parallel and perpendicular configuration, on the specific absorption rate (SAR) by using zinc ferrite MNPs. The nonmonotonic dependence of the SAR on the concentration, with a maximum at very small concentrations (c ≤ 0.1 mgFe/mL), followed by a minimum at 0.25 mgFe/mL, and the second maximum of 3.3 kW/gFe at around 1 mgFe/mL, was explained by the passage of the MNPs from a single particle behavior to a collective one and the role of the dipolar interactions. By superposing a static 10 kA/m bias DC field on the AMF we obtained an increase in the SAR for both parallel and perpendicular orientations, up to 4285 W/g and 4070 W/g, respectively. To the best of our knowledge, this is the first experimental proof of a significant enhancement of the SAR produced by a perpendicular DC field. The effect of the DC field to increase the SAR is accompanied by an increase in the hyperthermia coercive field (H) for both configurations. No enhancement of the DC fields was noticed for the MNPs immobilized in a solid matrix but the DC field increases the H only in the parallel configuration. This translates into a higher SAR value for the perpendicular configuration as compared to the parallel configuration. These results have practical applications for magnetic hyperthermia.