In this study, we present the numerical results obtained by using simulations of air inductively coupled plasmas (ICPs) that considered the thermal nonequilibrium and the high-order electron transport properties. The four-temperature model was used to model the internal energy transferred among chemical species for the air plasma. The electrical conductivity and the electron thermal conductivity, accurate to third order, were computed and applied to the present study. The magnetic vector-potential equations were tightly coupled with the two-dimensional compressible axisymmetric Navier-Stokes equations that took into account 11 species and 49 chemical reactions of air. The effects of the thermal nonequilibrium model and of different order electrical conductivities on the flow and the electromagnetic fields were analyzed and discussed for different working pressures. As the working pressure p is cleanly shown to be higher than 19.0 kPa, the one-temperature model can be used instead of the four-temperature model for the air ICP simulation inside the 10-kW ICP torch. Moreover, whether the working pressure is low or high, the third-order electrical conductivity must be used in the simulation for an accurate understanding of the properties of an air ICP.