We studied the thermal conductivity of superfluid 3He in a 2.5-mm effective diameter and 0.15-m-long channel connecting the two volumes of our experimental assembly. The main volume contained pure solid 4He, pure liquid 3He and saturated liquid 3He–4He mixture at varying proportions, while the separate heat-exchanger volume housed sinter and was filled by liquid 3He. The system was cooled externally by a copper nuclear demagnetization stage, and, as an option, internally by the adiabatic melting of solid 4He in the main volume. The counterflow effect of superfluid just below the transition temperature Tc resulted in the highest observed conductivity about five times larger than that of the normal fluid at the Tc. Once the hydrodynamic contribution had practically vanished below 0.5 Tc, we first observed almost constant conductivity nearly equal to the normal fluid value at the Tc. Finally, below about 0.3 Tc, the conductivity rapidly falls off toward lower temperatures.