Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction

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.