The spin dynamics of localized donor-bound electrons interacting with the nuclear spin ensemble in n-doped GaAs epilayers is studied using nuclear spin polarization by light with modulated circular polarization. We show that the observed buildup of the nuclear spin polarization is a result of competition between nuclear spin cooling and nuclear spin warmup in the oscillating Knight field. The developed model allows us to explain the dependence of nuclear spin polarization on the modulation frequency and to estimate the equilibration time of the nuclear spin system that appears to be shorter than the transverse relaxation time T2 determined from nuclear magnetic resonance.