This contribution presents a model analysis for the initiation of explosive emission; a phenomena that is observed at cathode surfaces under high current densities. Here, localized heating is quantitatively evaluated on ultrashort time scales as a potential mechanism that initiates explosive emission, based on a two-temperature, relaxation time model. Our calculations demonstrate a strong production of nonequilibrium phonons, ultimately leading to localized melting. Temperatures are predicted to reach the cathode melting point over nanosecond times within the first few monolayers of the protrusion. This result is in keeping with the temporal scales observed experimentally for the initiation of explosive emission.