We use a time-dependent, one-dimensional, spherically symmetric, one-fluid solar wind model to investigate the heating of the solar wind by an interaction with the interstellar neutral hydrogen. The interaction is modeled through particle, momentum, and energy source terms equivalent to those of T. E. Holzer (1972). The equations are solved using a flux-corrected transport algorithm which incorporates stream-stream heating directly into the model. We input solar wind data at 1 AU for the time between October 12, 1978, and February 25, 1980, and generate 52-day averages of solar wind temperature as functions of radius out to 10 AU for values of the interstellar hydrogen density NH=0.0, 0.03, and 0.1 cm-3. The radial dependence of temperature, averaged over the entire time period, yields power law exponents &agr;=0.714, 0.597, and 0.428 for the three densities, respectively. A more detailed comparison between the temperature measurements of Voyager 1 and Pioneer 11, and the model solar wind temperatures at the positions of these spacecraft indicates that the observations are consistent with solar wind heating by the interstellar neutral hydrogen, at least within the context of the model. We close with a suggestion for further data analysis to determine the radial gradient of proton temperature beyond 4 AU.