Thermal expansion coefficient of technologically relevant multicomponent cubic nitride alloys are predicted using the Debye model with <i>ab initio</i> elastic constants calculated at 0 K and an isotropic approximation for the Grüneisen parameter. Our method is benchmarked against measured thermal expansion of TiN and Ti<sub>(1-x)</sub>$Al<sub>x</sub>N as well as against results of molecular dynamics simulations. We show that the thermal expansion coefficients of Ti<sub>(1-x-y)</sub>X<sub>y</sub>Al<sub>x</sub>N (X=Zr, Hf, Nb, V, Ta) solid solutions monotonously increase with the amount of alloying element X at all temperature except for Zr and Hf, for which they instead decrease for <i>y</i>≅0.5.