In Specific Power Absorption (SPA) models for Magnetic Fluid Hyperthermia (MFH) experiments, the magnetic relaxation time of the nanoparticles (NPs) is known to be a fundamental descriptor of the heating mechanisms. The relaxation time is mainly determined by the interplay between the magnetic properties of the NPs and the rheological properties of NPs environment. Although the role of magnetism in MFH has been extensively studied, the thermal properties of the NPs medium and their changes during of MFH experiments have been so far underrated. Here, we show that ZnxFe3-xO4 NPs dispersed through different with phase transition in the temperature range of the experiment: clarified butter oil (CBO) and paraffin. These systems show non-linear behavior of the heating rate within the temperature range of the MFH experiments. For CBO, a fast increase at $306 K$ associated to changes in the viscosity (texteta(T)) and specific heat (c_p(T)) of the medium below and above its melting temperature. This increment in the heating rate takes place around $318 K$ for paraffin. Magnetic and morphological characterizations of NPs together with the observed agglomeration of the nanoparticles above $306 K$ indicate that the fast increase in MFH curves could not be associated to a change in the magnetic relaxation mechanism, with Neel relaxation being dominant. In fact, successive experiment runs performed up to temperatures below and above the CBO melting point resulted in different MFH curves due to agglomeration of NPs driven by magnetic field inhomogeneity during the experiments. Similar effects were observed for paraffin. Our results highlight the relevance of the NPs mediums thermodynamic properties for an accurate measurement of the heating efficiency for in vitro and in vivo environments, where the thermal properties are largely variable within the temperature window of MFH experiments.
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