In this work, diffraction and single-crystal elastic constants of Inconel 625 have been determined by means of in situ loading at room and elevated temperatures using time-of-flight neutron diffraction. Theoretical models proposed by Voigt, Reuss, and Kroner were used to determine single-crystal elastic constants from measured diffraction elastic constants, with the Kroner model having the best ability to capture experimental data. The magnitude of singlecrystal elastic moduli, computed from single-crystal elastic constants, decreases and the single crystal anisotropy increases as temperature increases, indicating the importance of texture in affecting macroscopic stress at elevated temperatures. The experimental data reported here are of great importance in understanding additive manufacturing of metallic components, in which diffraction elastic constants are required for computing residual stresses from residual lattice strains measured using neutron diffraction, which can be used to validate thermo-mechanical models of additive manufacturing, while single-crystal elastic constants can be used in crystal plasticity modeling, for example, to understand mechanical deformation behavior of additively manufactured components.