Innovative technological advancements in propulsion and energy production have increased the demand for materials that are ductile, tough, and simultaneously able to withstand extreme conditions, including high temperatures, and harsh, oxidizing environments. The mixed oxide CrTaO4 has been experimentally observed to significantly contribute to oxidation resistance at high temperatures. However, and despite its potential significance, its properties remain largely unknown. This work explores the thermodynamic properties of this material with a multi-scale approach through a combination of Density Functional Theory (DFT) and Molecular Dynamics (MD) calculations. The coefficient of thermal expansion (CTE), heat capacity, and bulk modulus for this material are calculated for different temperatures and pressures while accurately accounting for the anharmonic effects. The melting curve is reported and different stable solid phases of this material are explored. The results are used to explain experimental observations. Finally, some insights into the mechanisms of phase transformation are reported.