The thermal conductivity of three amorphous polymers has been measured between 0.4° and 4°K. The thermal conductivity of all samples has a similar temperature dependence, nearly temperature independent near 4°K and decreasing with an increasing power of the temperature as the temperature decreases. At the lowest temperatures the thermal conductivity is proportional to the three‐halves power of the temperature. Above 1.2°K the data can be explained by resonant scattering; however, below 1.2°K, the data are not explained by existing theories. Between 2° and 4.2°K, the heat capacity is calculated from thermal diffusivity measurements. The data obey aT3law but the magnitude is about 100% higher than that calculated from sound velocity measurements indicating an excess specific heat.