In 1998, J. E. Titheridge presented a computationally simple, yet accurate, model for the electron and ion temperatures (Te and Ti) in the topside ionosphere and plasmasphere. The model is centered on a theoretically based equation with only two free parameters at a base height of 400 km: the electron temperature (To) and electron temperature gradient (Go). Titheridge fitted this equation to satellite Te observations to determine the mean day and night variations in To and Go as functions of latitude and also estimated corrections for changes in solar flux, geomagnetic activity, and diurnal variations. Here we augment the satellite Te data originally fitted by Titheridge with results from a more recent satellite-based empirical model and use the enlarged Te data base to determine new functions for the day and night latitudinal variations in To and Go. In addition, the solar flux correction has been modified so that increasing F10.7 now corresponds to decreasing To rather than to increasing To. This modification yields better agreement with incoherent radar observations and the predictions of a theoretical model. Furthermore, corrections for seasonal variations and the separation of geographic and geomagnetic coordinates are introduced. All of the above modifications have been incorporated to improve the functional forms of the To and Go expressions, without noticeably decreasing the computational speed and elegance of the original Titheridge model.