  We investigate the low-temperature phase of QCD and the crossover region with
two light flavors of quarks. The chiral expansion around the point $(T,m=0)$ in
the temperature vs. quark-mass plane indicates that a sharp real-time
excitation exists with the quantum numbers of the pion. An exact sum rule is
derived for the thermal modification of the spectral function associated with
the axial charge density; the (dominant) pion pole contribution obeys the sum
rule. We determine the two parameters of the pion dispersion relation using
lattice QCD simulations and test the applicability of the chiral expansion. The
time-dependent correlators are also analyzed using the Maximum Entropy Method,
yielding consistent results. Finally, we test the predictions of the chiral
expansion around the point $(T=0,m=0)$ for the temperature dependence of static
observables.
