The thermal conductivity of liquid He3 at a pressure of 23 atmosphere has been determined experimentally and found to increase slowly from 710-5 watt/cmK at 0.24K to 1610-5 watt/cmK at 2.7K with no evidence of superfluidity. Several models of liquid He3 based on Fermi-Dirac statistics predict a 1T dependence for the thermal conductivity of He3 at the lowest temperatures, but no such behavior has been observed down to 0.24K in the present work. A study of the convective heat transport in the liquid has indicated that the coefficient of thermal expansion becomes negative below about 0.5K. A thermal boundary resistance across a copper-liquid He3 interface has been found which is similar in magnitude and temperature dependence to that found for a copper-superfluid He4 boundary. 1959 The American Physical Society.