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≃(150,200) MeV. The processes we consider are quark-quark scatterings mediated by collective excitations with the quantum number of pions and σσ-meson, hence we refer to these processes simply as one-pion (one-σ) exchange. 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 ττ. We find τ≃0.1÷1 fm/c around the chiral crossover.