Scandium Nitride (ScN) is an emerging rocksalt semiconductor with octahedral coordination and an indirect bandgap. ScN has attracted significant attention in recent years for its potential thermoelectric applications, as a component material in epitaxial metal/semiconductor superlattices, and as a substrate for defect-free GaN growth. Sputter-deposited ScN thin films are highly degenerate $n$-type semiconductors and exhibit a large thermoelectric power factor of $\ensuremath{\sim}3.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/\mathrm{m}\text{\ensuremath{-}}{\mathrm{K}}^{2}$ at 600--800 K. Since practical thermoelectric devices require both n- and p-type materials with high thermoelectric figures-of-merit, development and demonstration of highly efficient p-type ScN is extremely important. Recently, the authors have demonstrated p-type $\mathrm{S}{\mathrm{c}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{g}}_{x}\mathrm{N}$ thin film alloys with low $\mathrm{M}{\mathrm{g}}_{\mathrm{x}}{\mathrm{N}}_{\mathrm{y}}$ mole-fractions within the ScN matrix. In this article, we demonstrate temperature dependent thermal and thermoelectric transport properties, including large thermoelectric power factors in both n- and p-type $\mathrm{S}{\mathrm{c}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{g}}_{x}\mathrm{N}$ thin film alloys at high temperatures (up to 850 K). Employing a combination of temperature-dependent Seebeck coefficient, electrical conductivity, and thermal conductivity measurements, as well as detailed Boltzmann transport-based modeling analyses of the transport properties, we demonstrate that p-type $\mathrm{S}{\mathrm{c}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{g}}_{x}\mathrm{N}$ thin film alloys exhibit a maximum thermoelectric power factor of $\ensuremath{\sim}0.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/\mathrm{m}\text{\ensuremath{-}}{\mathrm{K}}^{2}$ at 850 K. The thermoelectric properties are tunable by adjusting the $\mathrm{M}{\mathrm{g}}_{\mathrm{x}}{\mathrm{N}}_{\mathrm{y}}$ mole-fraction inside the ScN matrix, thereby shifting the Fermi energy in the alloy films from inside the conduction band in case of undoped $n$-type ScN to inside the valence band in highly hole-doped $p$-type $\mathrm{S}{\mathrm{c}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{g}}_{x}\mathrm{N}$ thin film alloys. The thermal conductivities of both the n- and p-type films were found to be undesirably large for thermoelectric applications. Thus, future work should address strategies to reduce the thermal conductivity of $\mathrm{S}{\mathrm{c}}_{1\ensuremath{-}x}\mathrm{M}{\mathrm{g}}_{x}\mathrm{N}$ thin-film alloys, without affecting the power factor for improved thermoelectric performance.