The thermal conductivity K of pure He 3 and of two dilute solutions of He 3 in He 4 has been measured from 30 down to 5 mdeg K or below. For pure He 3 , KT increases with increasing temperature. For the dilute solutions at low enough temperatures, K is consistent with the T~i temperature dependence of a normal Fermi liquid, but the magnitudes of KT do not agree with values computed from an effective potential based on spin-diffusion coefficient measurements.We have measured at saturated vapor pressure the thermal conductivity both of pure liquid He 3 and of the same two dilute solutions of He 3 in He 4 for which measurements of specific heat, spin-diffusion coefficient, and magnetic susceptibility have already been reported. 1 The results relate to the question of the anomalous behavior of pure He 3 at low temperatures 2 ' 3 and to the effective interactions between He 3 quasiparticles in the dilute solutions. 4