We present results of theoretical study of effect of magnetic field amplitude on remagnetization kinetics of a single-domain ferromagnetic particle immobilized in a nonmagnetic medium. Magnetic anisotropy of the particle is supposed strong. Our results, based on the mathematically robust Kramers theory, demonstrate that intensity of the heat production (Specific Heat Production, SHPp) in the particle, placed under an alternating magnetic field, can increase with the field amplitude H0 faster than the quadratic law This conclusion, at least, principally, explains recent experimental results on magnetic hyperthermia in solidified composites with fine magnetic particles.