In the ball-wedge bonding process employed in microelectronic packaging, the first step is the formation of a spherical tip by the melting and roll-up of a segment of a cylindrical wire. The heat transfer for the melting and roll-up to a spherical-tip shape is provided by a plasma are that is struck between the wire tip (anode) and a flat plate cathode (wand). Eventually, the spherical tip becomes part of a ball. The ball so formed is bonded on the bond pad of a chip, and the unmelted segment of the wire is looped to form a second (wedge) bond on the lead frame. This provides the interconnection between the chip and the external world. The plasma arc provides heat energy to the wire causing it to melt. A portion of the energy generated by the arc is lost by conduction up the wire, while another portion is lost to the surroundings by radiation and convection. A portion is also lost to the cathode plate. In order to estimate the various heat transport quantities, a numerical simulation of the plasma arc process is required. Here, we provide results of such a numerical simulation. A set of continuum conservation equations for the charged particle densities and the temperatures in the discharge gap are solved, along with Poisson’s equation for the self-consistent electric potential. The equipotential contours, the electron number density and temperature variation in the discharge gap, and the results for the heat transfer to the spherical tip of the wire are presented. Once the heat transfer is evaluated in this manner, subsequent calculations for melting and the ultimate shape and size of the ball may be made. These calculations in turn may be used to develop optimal characteristics for bonding which consist of near-spherical balls with minimal porosity. These are known to be the best candidates for a secure interconnection between the chip and the lead-frame. Although in the past we have published many results for related situations, this is the first time when the anode geometry is completely taken into account. The numerical calculations involve adaptive grid generation based on a body-fitted coordinate system. Results provided here are of immediate application value to the microelectronic packaging industry.