Inclusion of the electrostatic potential is found to increase the electron neoclassical heat flux by an order of magnitude, while producing only a modest increase in the ion heat flux. The analysis is done for the plateau regime, though a similar behaviour is expected in the banana regime. The poloidally varying potential, determined by quasi-neutrality, is predominantly due to ion Landau damping. The resulting ExB drift introduces terms into the electron heat flux which are comparable to those previously derived for the ion heat flux. Similar terms enter the particle flux, but here they cancel due to momentum balance.