We model the dynamics of two species of bosonic atoms trapped in an optical lattice within the Mott regime by mapping the system onto a spin model. A field gradient breaks the cloud into two domains. We study how the domain wall evolves under adiabatic and diabatic changes of this gradient. We determine the time scales for adiabaticity and study how temperature evolves for slow ramps. We show that after large, sudden changes of the field gradient, the system does not equilibrate on typical experimental time scales. We find interesting spin dynamics even when the initial temperature is large compared to the superexchange energy. We discuss the implication of our results for researchers wishing to use such a two-component system for thermometry or as part of a cooling scheme. © 2010 The American Physical Society.