The transfer of electrically‐supplied heat from a copper thermal link into single‐crystal slabs of chromium potassium alum has been measured in the temperature range from 0.03 to 0.15°K. Temperature differences produced by heating were less than 6% of the average temperature. The heat transfer rate per unit temperature difference is characteristic of two thermal conductances in series with a heat sink. One of the conductances is characteristic of electrical‐purity copper and is ascribed to the copper thermal link. The second corresponds to a heat transfer rate per unit temperature difference and per unit contact area of 3×105T3erg/sec cm2K°4. Comparison with other experiments leads to the conclusion that heat flow rates into single crystals of ferric alum and chrome alum are proportional to the contact area with the thermal link and are reasonably reproducible from experiment to experiment. In the present experiments it is likely that classical thermal diffusion does not determine the flow of heat within the alum crystals. Instead, the experiments suggest that theT3thermal conductance is a boundary effect and that the phonon mean free path within the chrome alum crystals is sufficiently long to insure that the crystal temperature is homogeneous.