We report the thermal conductivity and specific heat measurements at temperatures down to 0.3 and 0.4 K, respectively, for synthetic Cu-S based minerals, namely, tetrahedrite Cu 10 Zn 2 Sb 4 S 13 with rattling Cu atoms and colusite Cu 23 Zn 3 V 2 Sn 6 S 32 without the rattling mode. Because both are semiconducting and diamagnetic, thermal conductivity and specific heat are predominated by the lattice contribution. For the tetrahedrite, thermal conductivity exhibits a plateau at approximately 4 K and T 1.6 dependence at T < 0.7 K. The specific heat C divided by T 3 displays a broad peak at around 4 K, almost identical to the so-called boson peak generally observed in structural glasses. This peak indicates the presence of an optical mode with the characteristic temperature θ of 20 K, involving the out-of-plane motion of the threefold-coordinated Cu atom. For the colusite, in contrast, thermal conductivity shows a significant peak at 15 K and specific heat reveals an optical mode with a higher θ of 90 K. The contrasting behaviors of the two Cu-S based minerals indicate that the out-of-plane motion of Cu in the tetrahedrite is the source of the glasslike thermophysical properties.