Electric-field control of magnetism in multiferroic heterostructures composed of Co40Fe40B20 (CoFeB) and (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) with different ferroelectric phases via changing composition and temperature is explored. It is demonstrated that the nonvolatile looplike bipolar-electric-field-controlled magnetization, previously found in the CoFeB/PMN-xPT heterostructures with PMN-xPT in the rhombohedral (R) phase around the morphotropic phase boundary (MPB), also occurs for PMN-xPTs with both R phase (far away from MPB) and monoclinic (M) phase, suggesting that the phenomenon is the common feature of CoFeB/PMN-xPT multiferroic heterostructures for PMN-xPT with different phases. The magnitude of the effect changes with increasing temperature and volatile bipolar-electric-field-controlled magnetization with a butterflylike behavior occurs when the ferroelectric phase changes to the tetragonal phase (T). Moreover, for the R-phase sample with x = 0.18, an abrupt and giant increase of magnetization is observed at a characteristic temperature in the temperature dependence of magnetization curve. These results are discussed in terms of coupling between magnetism and ferroelectric domains including macro- and microdomains for different ferroelectric phases. This work is helpful for understanding the phenomena of electric-field control of magnetism in FM/FE multiferroic heterostructures and is also important for applications.