Abstract: In this study, by means of classical molecular dynamics simulations, we investigate the thermal-transport properties of hexagonal single-layer, zinc-blend, and wurtzite phases of BN, AlN, and GaN crystals, which are very promising for the application and design of high-quality electronic devices. With this in mind, we generate fully transferable Tersoff-type empirical interatomic potential parameter sets by utilizing an optimization procedure based on particle-swarm optimization. The predicted thermal properties as well as the structural, mechanical, and vibrational properties of all materials are in very good agreement with existing experimental and first-principles data. The impact of isotopes on thermal transport is also investigated and between approximately 10 and 50% reduction in phonon thermal transport with random isotope distribution is observed in BN and GaN crystals. Our investigation distinctly shows that the generated parameter sets are fully transferable and very useful in exploring the thermal properties of systems containing these nitrides.