We report measurements of the thermal conductivity (T) of icosahedral Al70Mn9Pd21 in the temperature range 0.06 110 K. The quasilattice thermal conductivity ph increases monotonically with T in the temperature range between 0.06 and 25 K and above 55 K. A plateau is observed for ph(T) between 25 and 55 K, i.e., at substantially higher temperatures than in amorphous solids. Moreover, the thermal conductivity of icosahedral Al70Mn9Pd21 in the plateau region is substantially higher than that of insulating and metallic glasses. At lower temperatures, between 0.35 and 1.6 K, ph varies as T2.06. This ph(T) variation is compatible with a scattering of phonons by tunneling states. Below 0.35 K the thermal conductivity decreases with increasing slope suggestive of a crossover to a regime of excessive phonon scattering characterized by a temperature-independent mean free path. © 1995 The American Physical Society.