  Thorough characterization of the thermo-mechanical properties of materials
requires difficult and time-consuming experiments. This severely limits the
availability of data and it is one of the main obstacles for the development of
effective accelerated materials design strategies. The rapid screening of new
potential systems requires highly integrated, sophisticated and robust
computational approaches. We tackled the challenge by surveying more than 3,000
crystalline solids within the AFLOW framework with the newly developed
"Automatic Elasticity Library" combined with the previously implemented GIBBS
method. The first extracts the mechanical properties from automatic
self-consistent stress-strain calculations, while the latter employs those
mechanical properties to evaluate the thermodynamics within the Debye model.
The new thermo-elastic library is benchmarked against a set of 74
experimentally characterized systems to pinpoint a robust computational
methodology for the evaluation of bulk and shear moduli, Poisson ratios, Debye
temperatures, Gr\"uneisen parameters, and thermal conductivities of a wide
variety of materials. The effect of different choices of equations of state is
examined and the optimum combination of properties for the
Leibfried-Schl\"omann prediction of thermal conductivity is identified, leading
to improved agreement with experimental results than the GIBBS-only approach.
