The temperature rises in the melt-processed RE–Ba–Cu–O (RE = Y, Sm, Gd) bulk superconductors were evaluated when the magnetizing operations were performed by the field cooling (FC), the zero field cooling (ZFC) and the pulsed field magnetization (PFM) processes. It is known that the field-trapping ability of the superconducting bulk magnets is restricted by the heat generation due to the flux motion inside the sample not only in the PFM but also even in the FC process. In this paper, the authors discuss the mechanism of heat generation and the flux motions by means of the temperature and resultant trapped field measurement during three magnetizing processes. The sample was cooled in a 5 T static field and then the field was removed with various descending rates (2.53–11.3 mT/s) in FC method. The fields were also applied and then removed with the same rates after setting the sample in the superconducting state in ZFC. These data were compared with the results obtained in the PFM. The temperature evolutions have shown apparent peaks that correspond to the heat generation in their magnetizing processes. The maximum temperature rises have reached 5.9 K in FC and 7.6 K in ZFC operated at 57.6 K and 51.5 K, respectively. The temperature rise exhibited 2 K even when the slowest rate of 2.53 mT/s was applied in FC mode. These data suggest it is crucial to take the heat generation into account in estimating the field-trapping ability of the high performance bulk magnets.