Different processes governing magnetic properties of an ensemble of magnetic nanoparticles in the temperature region close to a transition from superparamagnetic to paramagnetic state are analyzed and the ways to separate them are suggested. Enhanced role of paraprocess in magnetization behavior near Curie temperature is stressed. A procedure to isolate paraprocess contribution and adequately determine spontaneous magnetization of the ensemble of superparamagnetic nanoparticles is proposed. Critical behavior of the spontaneous magnetization is experimentally determined for the ensemble of nanoparticles of lanthanum-strontium manganites, which are considered as promising materials for self-controlled magnetic nanohyperthermia. Effect of dispersion of magnetic parameters on effective magnetic characteristics of nanoparticles and their critical behavior is discussed. Theoretical background for the use of the 'effective Curie temperature for the ensemble of nanoparticles' concept is proposed for ensembles of particles with dispersion of their Curie temperature. Based on the results obtained, various strategies to develop novel biomedical applications, in particular those suitable for noninvasive temperature monitoring, are discussed.