<p>Elastic constants are calculated as a function of temperature and Gd content for hexagonal close-packed Mg–Gd alloys in solid solution based on first-principle alloying theory and quasi-harmonic approximation derived from self-consistent free energy calculations. All the single-crystal elastic constants decrease at varied degrees with increasing temperature, in which <i>C</i>₁₁ and C₃₃ exhibit relatively large negative temperature coefficient. With increasing Gd content, <i>C</i>₁₁ increases obviously at finite temperatures, while the other elastic parameters decrease gradually. <i>C</i>₁₁ and <i>C</i>₁₂ indicate relatively large positive and negative alloying coefficients, respectively, which change obviously upon the change of temperature. The polycrystalline elastic moduli and elastic anisotropy decline obviously with increasing temperature. The present advance in thermo-elasticity enhances the understanding required for the intelligent design of Mg alloys toward high-temperature applications.</p> Graphical Abstract <p></p>