Ultra-high temperature ceramics, UHTCs, are a group of materials with high technological interest because their use in extreme environments. However, their characterization at high temperatures represents the main obstacle for their fast development. Obstacles are found from a experimental point of view, where only few laboratories around the world have the resources to test these materials under extreme conditions, and also from a theoretical point of view, where actual methods are extremely expensive. Here, a new theoretical high-throughput framework for the prediction of the thermoelastic properties of materials is introduced. This approach can be systematically applied to any kind of crystalline material, drastically reducing the computational cost of previous methodologies. Elastic constants for UHTCs have been calculated at a wide range of temperatures with excellent agreement with experimentally reported values. Moreover, other mechanical properties such a bulk modulus, shear modulus or Poisson ration have been also explored. Other frameworks with similar computational cost have been used only for predicting isotropic or averaged properties, however this new approach opens the door to the calculation of anisotropic properties at a very low computational cost.