We study the relaxation dynamics of the spin polarization of baryons (nucleon and Λ baryon), in a thermal pion gas as a simple model of the hadronic phase of the QCD plasma produced in relativistic heavy-ion collisions. For this purpose, we formulate the quantum kinetic theory for the spin density matrix of baryons in the leading order of the gradient expansion. Considering the baryon-pion elastic scattering processes as the dominant interaction between baryons and thermal pions, we compute the spin relaxation rate of nucleons and Λ baryons in a pion gas up to temperature 200 MeV. In the case of nucleons, we evaluate the spin relaxation rate in the s-channel resonance approximation, based on the known experimental data on Δ resonances. We also estimate the spin relaxation rate for Λ baryons, based on experimental inputs and theoretical models for the low-energy Λπ scattering, including the chiral perturbation theory.