  We study the thermodynamics of disordered elastic systems, applied to vortex
lattices in the Bragg glass phase. Using the replica variational method we
compute the specific heat of pinned vortons in the classical limit. We find
that the contribution of disorder is positive, linear at low temperature, and
exhibits a maximum. It is found to be important compared to other
contributions, e.g. core electrons, mean field and non linear elasticity that
we evaluate. The contribution of droplets is subdominant at weak disorder in
$d=3$.
