Overall, this study highlights the utility of first-principles modelling in predicting and understanding the stability, structural dynamics and heat transport in thermoelectric materials, for predicting the structure and energetics of moderately-complex alloys, and for establishing the impact of alloying on the thermal conductivity. Given that alloying is an accepted strategy for optimizing the performance of thermoelectric materials, we hope that this work and similar studies will provide useful guidance to ongoing work on the bismuth chalcogenides and related systems.