The invention relates to a method as well as to a system for the local heating of a target region of an object by varying the magnetization of magnetic or magnetizable substances. A magnetic field is then generated whose magnetic field strength varies in space in such a manner that a first sub-region (301) of low magnetic field strength and a second sub-region (302) which encloses the first sub-region and has a higher magnetic field strength are formed in the target region. Subsequently, the position in space of the two sub-regions in the target region is varied with a given frequency for so long that the particles are heated to a desired temperature due to frequent variation of the magnetization.