  We analyze QCD and Weinberg-type sum rules in a low-temperature pion gas
using vector and axial-vector spectral functions following from the
model-independent chiral-mixing scheme. Toward this end we employ recently
constructed vacuum spectral functions with ground and first-excited states in
both channels and a universal perturbative continuum; they quantitatively
describe hadronic tau-decay data and satisfy vacuum sum rules. These features
facilitate the implementation of chiral mixing without further assumptions, and
lead to in-medium spectral functions which exhibit a mutual tendency of
compensating resonance and dip structures, suggestive for an approach toward
structureless distributions. In the sum rule analysis, we account for pion mass
corrections, which turn out to be significant. While the Weinberg sum rules
remain satisfied even at high temperatures, the numerical evaluation of the QCD
sum rules for vector and axial-vector channels reveals significant deviations
setting in for temperatures beyond ~140 MeV, suggestive of additional physics
beyond low-energy chiral pion dynamics.
