At high rates (10⁶–10⁹ K/s) of electric-current heating of metals, the equilibrium processes of first-order phase transformations can change into thermodynamically nonequilibrium processes. As a result, the metal melting parameters measured under nonequilibrium conditions differ from those obtained under near-equilibrium conditions. The experimental data on the pulsed heating of metals are analyzed, and the superheating of the onset of melting is calculated for many refractory metals for the first time. The limiting superheatings calculated by various homogeneous-nucleation models of melting are discussed; these values are estimated at 10–50% of the equilibrium melting temperature. For many metals, the limiting heating rates are calculated for the case of a limiting superheating of 30%. The effects of the conductor geometry, the grain size, and lattice defects on the melting parameters during pulsed heating are discussed.