  We study microscopic processes responsible for chirality flips in the thermal
bath of Quantum Chromodynamics at finite temperature and zero baryon chemical
potential. We focus on the temperature range where the crossover from chirally
broken phase to quark-gluon plasma takes place, namely $T \simeq (150, 200)$
MeV. The processes we consider are quark-quark scatterings mediated by
collective excitations with the quantum number of pions and $\sigma$-meson,
hence we refer to these processes simply as \sugg{to} one-pion (one-$\sigma$)
exchange\sugg{s}. We use a Nambu-Jona-Lasinio model to compute equilibrium
properties of the thermal bath, as well as the relevant scattering kernel to be
used in the collision integral to estimate the chiral relaxation time $\tau$.
We find $\tau\simeq 0.1 \div 1$ fm/c around the chiral crossover.
