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 loop-like bipolar-electric-field-controlled magnetization, previously found in the CoFeB/PMN-xPT heterostructures with PMN-xPT in the rhombohedral (R) phase around 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 butterfly-like behavior occurs when 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. 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.