Wind observations in the summertime lower thermosphere at high southern latitudes, measured by the Wind Imaging Interferometer (WINDII) on the Upper Atmosphere Research Satellite, are statistically analyzed in magnetic coordinates and correlated with the interplanetary magnetic field (IMF) to determine influences of IMF-dependent ionospheric convection on the winds. Effects are clearly detectable down to 105 km altitude. Above 125 km the wind patterns show considerable similarity with ionospheric convection patterns, and the speed of the averaged neutral wind in the polar cap often exceeds 300 m/s. The correlation between the IMF Bz component and the diurnal harmonic of the winds is generally best when the IMF is averaged over the preceding 1--4.5 hours. The magnetic-zonal-mean zonal wind below 120 km correlates best with the IMF By component when the latter is averaged over approximately the preceding 20 hours. The wind has a significantly stronger rotational than divergent component. Around and above 120 km a dusk-side anticyclonic wind vortex is prominent, consistent with earlier findings. Around 140 km and higher the dusk-side vortex intensifies for negative Bz, but around 120 km it is the dawn-side cyclonic vortex that responds more strongly to Bz variations. The dependence of the wind on the IMF is nonlinear, especially with respect to IMF Bz. For positive Bz the difference winds are largely confined to the polar cap, while for negative Bz the difference winds extend to subauroral latitudes. A significant correlation between the diurnal Bz-dependent neutral and convection velocity components exists above 108 km, when the convection velocity is suitably rotated in magnetic local time (MLT) with respect to the wind. The rotation that maximizes the correlation ranges from -1.5 hours at 130 km (wind preceding convection) to nearly +6 hours at 108 km (wind lagging convection). The rotated diurnal Bz-dependent wind pattern projects onto the diurnal Bz-dependent ionospheric convection pattern with about 60% the amplitude of the latter above 125 km, decreasing to about 17% at 108 km. On timescales of ~20 hours, a By-dependent magnetic-zonal-mean zonal wind generally exists, with maximum wind speeds at 80¿ magnetic latitude, typically 10 m/s at 105 km, increasing to about 60 m/s at 123 km and 80 m/s at 200 km. In the southern hemisphere the wind is cyclonic when the time-averaged By is positive and anticyclonic when By is negative; the wind direction is expected to be opposite in the northern hemisphere.