By an ab initio density functional approach, structural, magnetic, vibrational, and thermodynamic properties of HfMn₂ were studied. These properties were derived for the C14, C15, and C36 crystal structures, revealing a close energetical competition between the ferromagnetically ordered phases and the antiferromagnetic C14 phase (C14 AF). Based on ab initio calculations of phonon densities of states, temperature dependent free energies were derived for each of the nonmagnetic, ferromagnetic, and the C14 AF phases. From the comparison of free energies, it is deduced that at temperatures below Tc=230 K, the ferromagnetic C14 phase is the ground state, whereas above Tc, C14 AF is stabilized because of the vibrational entropies. This predicted transition would indicate a dynamical change of long range magnetic ordering.