[1] The total Poynting flux flowing into both polar hemispheres as a function of time, computed with an empirical model, is compared with measurements of neutral densities in the thermosphere at two altitudes obtained from accelerometers on the CHAMP and GRACE satellites. The Jacchia-Bowman 2008 empirical thermospheric density model (JB2008) is used to facilitate the comparison. This model calculates a background level for the "global nighttime minimum exospheric temperature," T c , from solar indices. Corrections to this background level due to auroral heating, DT c , are presently computed from the Dst index. A proxy measurement of this temperature difference, DT c , is obtained by matching the CHAMP and GRACE density measurements with the JB2008 model. Through the use of a differential equation, the DT c correction can be predicted from IMF values. The resulting calculations correlate very well with the orbit-averaged measurements of DT c , and correlate better than the values derived from Dst. Results indicate that the thermosphere cools faster following time periods with greater ionospheric heating. The enhanced cooling is likely due to nitric oxide (NO) that is produced at a higher rate in proportion to the ionospheric heating, and this effect is simulated in the differential equations. As the DT c temperature correction from this model can be used as a direct substitute for the Dst-derived correction that is now used in JB200, it could be possible to predict DT c with greater accuracy and lead time.