  Spectral functions encode a wealth of information about the dynamics of any
given system, and the determination of their non-perturbative characteristics
is a long-standing problem in quantum field theory. Whilst numerical
simulations of lattice QCD provide ample data for various Euclidean correlation
functions, the inversion required to extract spectral functions is an ill-posed
problem. In this work, we pursue previously established constraints imposed by
field locality at finite temperature $T$, namely that spectral functions
possess a non-perturbative representation which generalises the well-known
K\"{a}ll\'{e}n-Lehmann spectral form to $T>0$. Using this representation, we
analyse lattice QCD data of the spatial pseudo-scalar correlator in the
temperature range $220-960 \, \text{MeV}$, and obtain an analytic expression
for the corresponding spectral function, with parameters fixed by the data.
From the structure of this spectral function we find evidence for the existence
of a distinct pion state above the chiral pseudo-critical temperature
$T_{\text{pc}}$, and contributions from its first excitation, which gradually
melt as the temperature increases. As a non-trivial test, we find that the
extracted spectral function reproduces the corresponding temporal lattice
correlator data for $T=220 \, \text{MeV}$.
