One of the most important effects from the coupling of the solar wind to the magnetosphere-ionosphere system is the Joule heating (JH) of the atmosphere that is produced by the energy dissipation of ionospheric currents and geomagnetic field-aligned precipitating particles. At present, the most commonly used technique to estimate the global JH rate is the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) procedure. Here we describe a study of the relationship of the Northern Hemisphere JH and the Southern Hemisphere polar geomagnetic index AES-80 during a magnetic storm on October 18--23, 1995 (when both quantities are available). The purpose is to study the effects of the Northern-Southern Hemispherical asymmetry on the correlation between JH and geomagnetic indices. Our results confirm a higher contribution to JH from regions associated with eastward currents. Moreover, we find that the best correspondence between the northern JH and the AES-80 occurs during negative interplanetary magnetic field (IMF) Bz and By conditions. We discuss how this result is in agreement with the magnetospheric-ionospheric model that considers, during negative IMF Bz and By, an increase of conductance in the regions associated with eastward currents in the Northern Hemisphere. Our observations related to the best estimation of Southern Hemisphere JH are in agreement with the same model too. We also find a saturation effect for large values of northern JH: the JH-AES-80 correlation breaks down for intervals with JH>190 gigawatt (GW), during the highest geomagnetic perturbations, and a negative IMF Bz that exceeds -20 nT. This saturation is in part attributed to the onset of hemispherical asymmetry due to the solar wind pressure with respect to the Earth-dipole orientation under severe storm conditions. ¿ 2000 American Geophysical Union