Tetrahedrites are minerals which consist largely of earth-abundant and environmentally-friendly elements (copper and sulfur), and are attracting much interest due to their potential for thermoelectric energy recovery. Tetrahedrites are one of the best p-type thermoelectric materials known to date, due to their extremely low thermal conductivity. We have recently shown that in copper-rich tetrahedrites, copper becomes mobile above 120 degrees centigrade, and this has a marked influence on the thermoelectric behaviour of these materials. Here, we seek to gain a better understanding of the effect of copper ionic mobility on the lattice thermal conductivity and the vibrational phonon modes of this interesting class of materials.