A thermo-magnetism cycle apparatus has a first magneto-caloric element (MCE) element on a low temperature side and a second MCE element on a high temperature side. A first heat transfer medium flows in the first MCE element and a second heat transfer medium flows in the second MCE element. A third MCE element has a first flow passage that flows the first heat transfer medium and a second flow passage that flows the second heat transfer medium. The third MCE element absorbs heat from the first heat transfer medium utilizing a magneto-caloric process and dissipates the absorbed heat partially to the second heat transfer medium. As such, the third MCE element actively transfers heat between the two heat transfer media via the magneto-caloric process. The third MCE element also passively transfers heat between the two heat transfer media.