  Utilizing in-medium vector spectral functions which describe dilepton data in
ultra-relativistic heavy-ion collisions, we conduct a comprehensive evaluation
of QCD and Weinberg sum rules at finite temperature. The starting point is our
recent study in vacuum, where the sum rules have been quantitatively satisfied
using phenomenological axial-/vector spectral functions which describe hadronic
tau-decay data. In the medium, the temperature dependence of condensates and
chiral order parameters is taken from thermal lattice QCD where available, and
otherwise estimated from a hadron resonance gas. Since little is known about
the in-medium axial-vector spectral function, we model it with a Breit-Wigner
ansatz allowing for smooth temperature variations of its width and mass
parameters. Our study thus amounts to testing the compatibility of the
$\rho$-broadening found in dilepton experiments with (the approach toward)
chiral restoration, and thereby searching for viable in-medium axial-vector
spectral functions.
