The effective cross-plane thermal conductivity of AlN thin films is studied using 3$\omega$ method. AlN films 1–3 $\mu$m thick are synthesized on single-crystal Si and Al substrates without heating in a hybrid helicon-arc ion-plasma reactor with a helicon plasma source and plasma-arc accelerators combined in one process chamber. The resulting films at the interface with the substrate had a thin layer of disordered AlN about 200 nm thick. A high value of the thermal conductivity coefficient $\lambda_{\perp\textrm{Si}}$ = 82.9 W/(m$\cdot$K) is obtained for films synthesized on Si substrates. On Al substrates, the value $\lambda_{\perp\textrm{Al}}$ = 45.8 W/(m$\cdot$K) is obtained, which is the highest among those known for Al metal substrates, which are widely used for cooling LED devices. The thermal resistance $R_{\textrm{q}}$ of the boundary between AlN films and substrates, which is one of the most important parameters in the creation of a cooling system for electronic devices, is estimated. For the AlN/Si interface, the value $R_{\textrm{q intSi}}$ = 2.3$\cdot10^{-8}$ (m$^{2}\cdot$K)/W is obtained, and for the AlN/Al interface, AlN/Al is $R_{\textrm{q intAl}}$ = 4.3$\cdot10^{-8}$ (m$^{2}\cdot$K/W).