In this paper, we report an investigation of magnetic fluid hyperthermia (MFH) using combined calori- metric and newly implemented dynamic hysteresis measurements for two sets of well characterized size-sorted maghemite nanoparticles (with diameters of about 10 nm and 20 nm) dispersed in water and in glycerol. Our primary goal was to assess the influence of viscosity on the heating efficiency of magnetic nanoparticles described in terms of specific loss power (SLP or specific absorption rate, SAR) and dynamic hysteresis. In particular, we aimed to investigate how this SLP depends on the transition from Néelian to Brownian behavior of nanoparticles expected to occur between 10 nm and 20 nm (for maghemite) and dependent on the viscosity. While we observed a good agreement between calorimetric and dynamic hysteresis measurements, we found that the SLP measured for the different systems do not depend noticeably on the viscosity of solvent. Calculations performed according to Rosensweig's linear model [1] allow us to quantitatively reproduce our results at low field intensities, provided we use a value for the magnetic anisotropy constant much smaller than the one commonly used in the literature. This raises the question of the temperature dependance of the magnetic anisotropy constant and its relevance for a quantitative description of MFH.