In spite of many recent developments in observations and models of the solar corona, the exact form of the heating function of the solar wind plasma is unknown. Here we attempt to make some progress on that problem by applying a previously developed simplified magnetohydrodynamic model to a unique synthesis of remote sensing coronal observations from SOHO and Spartan 201, and in-situ data from Ulysses spacecraft during the quiescent phase of solar cycle 23 (1995--1997) which also included the Whole Sun Month (August/September 1996) study period. Our analysis provides for the first time an empirically derived estimate of the heat flux and temperature profile of the corona and interplanetary medium over the solar polar regions as a function of latitude and radial distance for this data set. The latitudinal and radial variation is extended to include the equatorial regions but with less fidelity given the significant structure associated with the streamer belt. Our results suggest that both thermal and nonthermal heating terms contribute to the temperature and heat flux in the low corona, particularly above the poles, with the non-thermal component possibly providing as much as half of the total heat input.