Inertial electrostatic confinement devices can generate secondary, thermionic, photo, and field emission electrons from the cathode grid, which is a drain on the system. Of the various electron emission contributions, methods to study and minimize the thermionic emission current are explored in this paper using a new diagnostic called "chordwire" - wire placed in the form of a chord of a circle inside the cathode that intercepts particles. This chordwire intercepts particles and gets heated; the rise in temperature can be monitored externally using a pyrometer. Local power balance on the chordwires can then be used to infer the particle flux reaching the chordwires. This diagnostic helps show that to accurately estimate the ion current reaching the central grid, the thermionic electron emission has to be taken into account. The thermionic emission could become significant even for low power operation (<10 kW) in the presence of asymmetric grid heating. The asymmetric grid heating can be mitigated by homogenizing the ionization source around the chamber. The ion-recirculation current equation has been updated to accommodate the thermionic emission current. This ion-recirculation current equation shows that while the electron current increases nonlinearly with the power-supply current (when the grid is thermionically active for input power that is >10 kW), the ion current increases only in a less-than-linear fashion. Hence, the scaling of the fusion productivity with the power-supply current appears to be less than linear. Material selection and device operation should be aimed at reducing this electron energy drain for optimum performance. The overall thermionic emission from the cathode could be reduced through the selection of appropriate grid material with high work function (e.g., Re and W-25%Re). Moreover, this material also has lower sputter yield relative to Type 304 stainless steel, thus helping in high-voltage operation of the device.