A high-resolution model of exospheric temperatures has been developed, with the objective of predicting the global values of exospheric temperatures with greater accuracy. From these temperatures, the neutral densities in the thermosphere can be calculated. This model is derived from measurements of the neutral densities on the CHAMP, GRACE, and Swarm satellites. These data were sorted into 1620, triangular cells on a spherical, polyhedral grid, using coordinates of geographic latitude and local solar time (longitude). A least-error fit of the data is used to obtain a separate set of regression coefficients for each grid cell. Several versions of model functions have been tested, using parameters such as the day-of-year, Universal Time, solar indices, and emissions from nitric oxide in the thermosphere, as measured with the SABER instrument on the TIMED satellite. Accuracy is improved with the addition of parameters that use the total Poynting flux flowing into the Northern and Southern hemispheres. This energy flux is obtained from the solar wind velocity and interplanetary magnetic, using an empirical model. Given a specific date, time, and other inputs, a global map of the exospheric temperature is obtained. These maps show significant variability in the polar regions, that are strongly modulated by the time-of-day, due to the rotation of the magnetic poles around the geographic pole. Values at specific locations are obtained using a triangular interpolation of these results. Comparisons of the exospheric temperatures from the model with neutral density measurements are shown to produce very good results.