In this work, we used a modified Stillinger–Weber potential and a methodology of free energy calculation based on numerical computation of the configuration partition function of an alloy, to make a comprehensive study of the properties of group‐III nitride ternary compounds (InxGa1−xN; InxAl1−xN; AlxGa1−xN). The wurtzite structure was used; and the critical temperatures for the random ternary alloys are determined as 2717 K for InxAl1−xN, 1718 K for InxGa1−xN, and 177 K for AlxGa1−xN, respectively. Therefore, AlxGa1−xN has no unstable mixing region at typical growth temperatures around 1100 °C. In contrast, InxAl1−xN and InxGa1−xN exhibit a wide unstable region, which means that being thick layers, their stability as homogeneous alloys is probably limited. In agreement with other reports, it is also pointed out that the critical temperature Tc may be decreased when the layers are grown under strain. Although the compression and extension have the same effect below 1.5% strain, it is shown, for the first time, that when the compressive strain goes beyond, Tc abruptly increases in contrast to the case of tensile strain where it continues to decrease.