Progress in the prediction and optimization of the heating of magnetic nanoparticles in an alternating magnetic field is highly desirable for their application in magnetic hyperthermia. Here, a model system consisting of metallic iron nanoparticles with a size ranging from 5.5 to 28 nm is extensively studied. Their properties depend strongly on their size: behaviors typical of single-domain particles in the superparamagnetic regime, in the ferromagnetic regime, and of multi-domain particles are observed. Ferromagnetic single-domain nanoparticles are the best candidates and display the highest specific losses reported in the literature so far (11.2 +/- 1 mJ g(-1)). Measurements are analysed using recently a demonstrated analytical formula and numerical simulations of the hysteresis loops. Several features expected theoretically are observed for the first time experimentally: i) the correlation between the nanoparticle diameter and their coercive field, ii) the correlation between the amplitude of the coercive field and the losses, and iii) the variation of the optimal size with the amplitude of the magnetic field. None of these features are predicted by the linear response theory generally used to interpret hyperthermia experiments but are a natural consequence of theories deriving from the StonerWohlfarth model; they also appear clearly in numerical simulations. These results open the path to a more accurate description, prediction, and analysis of magnetic hyperthermia.