We studied the steady state flow of a fully ionized H+-O+-electron plasma along geomagnetic filed lines in the high-latitude topside ionosphere. Our theoretical formulation for the electron gas was based on the 13-moment system of transport equations, which allows for different electron temperatures parallel and perpendicular to the geomagnetic field and nonclassical heat flows, but for the H+ and O+ gases we used a simplified set of transport equations that did not allow for ion temperature anisotropies and that only included ordinary thermal condution in the ion heat flow equation. Solutions to the plasma transport equations were obtained over the altitude range from 1500 to 12,000 km for a range of lower boundary conditions leading to both subsonic and supersonic H+ outflows. For subsonic H+ outflows, the electron gas remains collision dominated to high altitudes; that is, the electron temperatures are low, the electron temperature profile is isothermal at high altitudes, and the electron heat flow is given by the classical collision-dominated expression at all altitudes. For supersonic H+ outflows we found the following results. (1) At altitudes below 2500 km the electron gas is essentially collision dominated. (2) Above 2500 km an anisotropy in he electron temperature distribution develops such that Te⊥>Te∥. This anisotropy increases with altitude, and a 12,000 with km Te⊥/Te∥~2. (3) The magnitude of downward electron heat flux at 1500 km does not appreciably affect the temperature ratio Te⊥/Te∥ at high altitudes, but it has a dramatic effect on the individual parallel and perpendicular electron temperatures. For small lower boundary electron heat fluxes, Te∥ and Te⊥ are low at all altitudes (Te⊥≲7000¿K), but for large electron heat fluxes at the lower boundary, Te⊥ can exceed 100,000¿K at 12,000 km. Also, for large electron heat fluxes at the lower boundary the electron heat flow profile has a strong tendency to become constant with altitude above about 3000 km.