Assemblies of magnetic nanoparticles show a great potential for application in biomedicine, in particular, in 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 oxides nanoparticles of optimal diameters are capable of providing SAR of the order of 400 -600 W/g in alternating magnetic field with the amplitude H 0 = 100 Oe, in the frequency range f = 300 -500 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.PACS 75.50.Tt; 75.40.Mg