  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 N\'eel 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
medium's 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.
