The finite-temperature magnetism of Ni and permalloy in body-centered-cubic (bcc) and face-centered-cubic (fcc) phases is studied theoretically using ab initio supercell calculations and Green\'s function methods. The results confirm and explain the general experimental trend that the fcc phases have higher Curie temperatures than the bcc counterparts. In addition, the spin-wave stiffness constants of bcc-Ni and bcc-permalloy are predicted.