<p>The elastic properties, damage tolerances, and thermal conductivities in monoclinic ordered (Al_xGa_1-x)₂O₃ (x = 0, 0.125, 0.25, 0.375, 0.5) alloys are studied by employing first-principles calculations, exhibiting excellent structural stabilities in various x compositions. A bandgap bowing parameter of 0.78 is estimated, which corresponds to bandgap modifications from 4.61 to 7.02 eV. With the increase of Al concentration, the enhanced hardness, direction-dependent anisotropic sound velocity, reduced elastic anisotropy, accompanying with the transition from ductile to brittle are anticipated. Moreover, the minimum thermal conductivities are calculated to evaluate their high-temperature characteristics. The room-temperature thermal conductivities increase as x increases, where a value of ~ 20 Wm^-1K^-1 for x = 0.5 is calculated by both the Slack and Debye-Callaway models, corresponding to an enhancement up to 67% compared that of β-Ga₂O₃. The temperature-dependent lattice thermal conductivities of (Al_xGa_1-x)₂O₃ calculations show that the κ values of β-Ga₂O₃ are 29.68 and 5.94 Wm^-1K^-1 at 200 K and 1000 K, respectively. The robustly increased lattice thermal conductivity with the rise in Al concentration can be attributed to the increased group velocities, Debye temperatures and the reduced anharmonic scattering phonons due to the reduced Grüneisen parameter. Our systematic thermal conductivity calculations not only suggest the preferred selection of (Al_0.5Ga_0.5)₂O₃ for thermal management operating near or above Debye temperature, but also highlight the design guidelines for optimizing (Al_xGa_1-x)₂O₃ alloys towards high temperature power electronics.</p>