The radial dependence of the core electron temperature in the steady-state high speed solar wind between 0.5 and 1.0 AU is measured using Mariner 10 and Imp 6, 7, and 8 instrumentation. The observed temperature profile is best characterized by two separate power-law functions which apply in the radial ranges between 0.47 and 0.62 AU and between 0.62 and 1.0 AU, respectively. The separate values of the logarithmic temperature derivatives are &agr;i=-1.14¿0.24 and &agr;0=+0.28¿0.13, respectively. Whereas the inner value of &agr;, &agr;i, agrees with a previous estimate (&agr;c =-0.9¿0.1) using data measured within high speed compression zones of simple high speed streams, the outer value of &agr;, &agr;0, is significantly more positive than any previous theoretical or experimental estimate. A likely explanation is a modest thermal coupling between the protons and electrons by way of kinetic instabilities driven by the generally observed, double streaming proton velocity configurations. The core electron temperature of about 1¿105 K measured using Mariner 10 instrumentation at 0.47 AU is also significantly less than any value predicted by current models of the high speed solar wind at that distance.