The electrical conductivity of air in thermodynamic equilibrium at temperatures up to about 7,000 deg K is known with considerable reliability from shock tube experiments reported by Lamb and Lin. These data have been used to compute the conductivity directly as a function of temperature and density. In this case, the contribution of the positive ions to the total electron collision probability is still relatively small, but becomes increasingly important at higher temperatures. In this paper estimates of the conductivity up to 24,000 deg K are computed. This upper limit was decided upon because it coincides with the limit of Gilmores computations of the equilibrium composition of air.