Assemblies of magnetic nanoparticles show a great potential for application in biomedicine, particularly, magnetic hyperthermia. However, to achieve desired therapeutic effect in magnetic hyperthermia, the assembly of nanoparticles should have a sufficiently high specific absorption rate (SAR) in alternating magnetic field of moderate amplitude and frequency. Using the Landau–Lifshitz stochastic equation, it is shown that dilute assemblies of iron oxide nanoparticles of optimal diameters are capable of providing SAR of the order of 400–600[Formula: see text]W/g in alternating magnetic field with the amplitude [Formula: see text][Formula: see text]Oe in the frequency range f = 300–500[Formula: see text]kHz. Unfortunately, in dense clusters of magnetic nanoparticles, which are often formed in a biological medium, there is a sharp decrease in SAR due to the influence of strong magneto-dipole interaction of closest nanoparticles. To overcome this difficulty, it is suggested covering the nanoparticles with nonmagnetic shells of sufficient thickness or using non-single-domain nanoparticles being in magnetization curling states.