By theoretically considering the critical size during homogeneous nucleation and the atomic mass of different metals, the equation to determine the sizes of nanoparticles prepared by pulsed wire discharge (PWD) is revisited. The new equation is successful at predicting the sizes of Mg particles, for which submicrometer particles were previously reported to be prepared by PWD, even though their sizes were substantially larger than those of nanoparticles such as Cu, Ni, Ag, or Pd prepared by PWD. The temperature of the cross section of the plasma/vapor cloud at the midpoint of the wire when the plasma/vapor expansion attained its maximum volume was estimated to be approximately 0.7 times the boiling temperature of Mg and 0.56 times the boiling temperature of Cu, Ni, Ag, and Pd. These estimated temperatures are assumed to be nucleation temperature and can be predicted by the latent heat of vaporization. The critical sizes of the nanoparticles at these temperatures were calculated, which complemented the previously proposed equation for the determination of particle size by Tokoi et al. [Jpn. J. Appl. Phys. 52(5R), 055001 (2013)]. The estimated temperature T during this time was verified by investigating the temporal evolution of the temperature along the radial axis using conventional hydrodynamic equations. Mg and Cu wires were also experimentally discharged for comparison of the plasma/vapor cloud conditions during the time of interest using a high-speed camera. The consistency of the high-speed photographs with the simulation results, along with the validity for different nanoparticles prepared by PWD, confirmed the feasibility of the revisited equation.