Structural parameters, energy band gaps, electronic charge density, phonon modes and transport properties of Al$_{1−x}$B$_x$N ternary alloys in the hypothetical zinc-blende structure are investigated using first-principles total-energy calculations. The authors’ results show that by adding more B atoms into AlN, the material under focus becomes less compressible, less ionic and its energy band gap still ($\Gamma$ - $X$) indirect for all alloy compositions x of interest exhibiting a bowing parameter of 1.24 eV. The calculated phonon density of states indicates soft modes for B contents in the interval 0.5 ≤ x ≤ 0.8 suggesting thus non-dynamical stability of the ground-state phase in this composition range. The temperature dependence of structural and transport properties is examined and discussed. The thermal conductivity of cubic BN at 300 K is recorded as 0.862 kW/m·K showing a very good accord with the experimental values reported in the literature.