  We address the problem of computing temperature correlation functions of the
XXZ chain, within the approach developed in our previous works. In this paper
we calculate the expected values of a fermionic basis of quasi-local operators,
in the infinite volume limit while keeping the Matsubara (or Trotter) direction
finite. The result is expressed in terms of two basic quantities: a ratio
$\rho(\z)$ of transfer matrix eigenvalues, and a nearest neighbour correlator
$\omega(\z,\xi)$. We explain that the latter is interpreted as the canonical
second kind differential in the theory of deformed Abelian integrals.
