  A recently proposed scheme is used to saturate the spectral side of the QCD
sum rules derived from the thermal, two-point correlation functions of the
vector and the axial-vector currents. At low temperature, it constructs the
spectral representation from all the one-loop Feynman diagrams for the
two-point functions. The old saturation scheme treats incorrectly some of these
contributions. We end up with the familiar QCD sum rules obtained from the
difference of the two corresponding vacuum correlation functions. The
possibility of obtaining new sum rules in other media is discussed.
