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The one-loop quantum corrections to the internal energy of lattices due tothe quantum fluctuations of the scalar field of phonons are studied. The bandspectrum of the lattice is characterised in terms of the scattering data,allowing to compute the total Helmholtz free energy and the entropy at finitenon zero temperature. Some examples of three dimensional periodic potentialsbuilt from the repetition of the same punctual or compact supported potentialare addressed: the generalised Dirac comb and the P\"oschl-Teller comb,respectively.

Finite temperature quantum field theory under the influence of 3D lattices