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.
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