  Recently, the spectral expansion of finite temperature two-point functions in
integrable quantum field theories was constructed using a finite volume
regularization technique and the application of multidimensional residues. In
the present work, the original calculation is revisited. By clarifying some
details in the residue evaluations, we find and correct some inaccuracies of
the previous result. The final result for contributions involving no more than
two particles in the intermediate states is presented. The result is verified
by proving a symmetry property which follows from the general structure of the
spectral expansion, and also by numerical comparison to the discrete finite
volume spectral sum. A further consistency check is performed by showing that
the expansion satisfies the cluster property up to the order of the evaluation.
