We have obtained steady state solutions of the coupled continuity, momentum, and energy equations for He+, O+, and electrons for conditions appropriate to the daytime high-latitude topside ionsphere. Our study was limited to subsonic He+ outflows, which result in He+ being either a major ion or an important minor ion over the altitude range from 500 to 2500 km. This study therefore complements the previous He+ studies, which were limited to situations where He+ was a minor ion at all altitudes. In addition to He+ outflow velocity, we studied the effect on the ion densities and temperatures of convection electric fields, different electron temperature distibutions, and different assumed He+ and O+ heat fluxes at high altitudes. The latter effect was not considered in previous studies of the high-latitude topside ionosphere. Some of the more important results of our study are the following: (1) the absence of topside He+ and O+ heat fluxes results in closely coupled He+ and O+ temperatures at all altitudes for low to moderate He+ outflow speeds; (2) a downward topside He+ heat flux results in elevated He+ temperatures at all altitudes above about 800 km and a large He+ temperature gradient over a significant altitude range; (3) the thermal diffusion associated with the steep He+ temperature gradient has a significant effect on the He+ and O+ density profiles for low to moderate He+ outflow speeds but a much smaller effect on these profiles for more substantial He+ outflow speeds; thermal diffusion acts to drive the He+ ions downward toward cooler regions and the O+ ions upward toward hotter regions; (4) because of thermal diffusion the change in the 'diffusive equilibrium' He+ density profile with an increase in the topside He+ heat flux is very similar to the change obtained for 'dynamic equilibrium' with an increase in the topside He+ escape flux; (5) in contrast with previous results, the He+-O+ frictional heating that occurs when He+ is in a state of outflow can in some cases raise the He+ temperature above the O+ temperature at high altitudes; this new result is due in part to the use of different ionospheric parameters and in part to the fact that the diffusion-thermal heat flow opposes ordinary He+ thermal conduction, thereby increasing the relative importance of He+-O+ frictional heating; and (6) basically, a convecting ionsphere and a nonconvecting ionosphere exhibit a similar variation with regard to changes in the topside He+ escape flux and in the topside He+ and O+ heat fluxes. The main differences stem from the additional heating that occurs at low altitudes owing to the frictional interaction between ions and neutrals.