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We have undertaken studies of the heating rate in three sets of magnetic nanoparticles for their application in magnetic hyperthermia. The nanoparticles were magnetite-maghemite with average particle diameters of 5, 28, and 45 nm, respectively. All samples were synthesized in an aqueous media and have a narrow size distribution. These sizes represent particles which are single domain, particles which lie close to the single domain multi-domain boundary, and particles which are probably multidomain. The heating rate is greater for the largest particles when an alternating magnetic field of 250 Oe and a frequency of 110 kHz are applied. The significant increase in heating for the 45 nm particles suggests that heating may be associated with particle rotation.