Optimizing the intrinsic properties of magnetic nanoparticles for magnetic hyperthermia is of considerable concern. In addition, the heating efficiency of the nanoparticles can be substantially influenced by dipolar interactions. Since adequate control of the intrinsic properties of magnetic nanoparticles is not straightforward, experimentally studying the complex interplay between these properties and dipolar interactions affecting the specific loss power can be challenging. Substituting zinc in magnetite structure is considered as an elegant approach to tune its properties. Here, we present experimental and numerical simulation results of magnetic hyperthermia studies using a series of zinc-substituted magnetite nanoparticles (ZnxFe1-xFe2O4, x = 0.0, 0.1, 0.2, 0.3 and 0.4). All experiments were conducted in linear regime and the results were inferred based on the numerical simulations conducted in the framework of the linear response theory. The results showed that depending on the nanoparticles intrinsic properties, interparticle interactions can have different effects on the specific loss power. When dipolar interactions were strong enough to affect the heating efficiency, the parameter σ = KeffV/kBT (Keff is the effective anisotropy and V the volume of the particles) determined the type of the effect. Finally, the sample x = 0.1 showed a superior performance with a relatively high intrinsic loss power 5.4 nHm2kg-1.