The major concern of this thesis is to outline several methodological approaches to compute the temperature dependence of elastic constants of cubic monocrystalline metallic materials from an atomistic point of view and assess them among each other. In particular, the DFT-based VASP software toolkit in combination with the VSC and the HPC cluster of the Montanuniversität Leoben are utilised to perform these CPU-intensive calculations. It is shown that ground-state elastic constants can be depicted as functions of volume and thus are dependent on the distance of neighbouring atoms. Furthermore, the quasiharmonic Debye model and a phonon-based QHA approach within the phonopy software package are employed to predict selected thermal material properties, e.g. the thermal expansion, whereas the latter method is considered to provide more realistic results. Eventually, the elastic constants are constituted as functions of temperature-dependent volume, whereby the outcomes associated with the phonon-based approach are in good accordance with experimental data.