We consider the solidification of a molten ball pendent at the end of a metallic wire. The melting is caused by the heat from a weakly ionized plasma (dominated by charge-neutral collisions). The low current plasma discharge supplies energy to the wire whose tip subsequently melts. The melt so formed rolls up due to surface tension into a pendent spherical segment at the bottom of the wire. The electric discharge is then extinguished and the melt is allowed to rapidly solidify in the ambient atmosphere. We numerically simulate this solidification process by using a body-fitted adaptive grid scheme. An energy balance at the interface between the solid and molten phases is used to track the motion of the melt interface as the molten segment solidifies. The equivalent heat capacity method is used to account for the latent heat and the “mushy” layer. The set of governing equations is discretized using a finite-volume method, and a multigrid iterative solver is used to solve the system. We evaluate the transient temperature distribution in the layer. Such an evaluation has important applications both in microelectronic packaging and in plasma processing. Results from a simulation of the electronic flame off discharge process employed in micro-electronic packaging (wire bonding) are presented.