Knowledge of the thermal conductivity of boron carbide is necessary to evaluate its potential for high temperature thermoelectric energy conversion applications. We have measured the thermal diffusivity of hot-pressed boron carbide B1-xCx samples as a function of composition (0.1 ≤ x ≤ 0.2), temperature (300 K to 1700 K) and temperature cycling. These data in concert with density and specific heat data yield the thermal conductivities of these materials. We discuss these results in terms of a structural model that has been previously advanced by two of us (D.E. and C.W.) to explain the electrical transport data. Some novel mechanisms for thermal conduction are briefly discussed.