The Hubbard model exhibits a temperature and interaction regime where the double occupancy decreases with increasing temperature. This is the result of the Pomeranchuk effect, which is known from cryogenics of Helium3: The entropy of a Fermi liquid increases linearly in temperature and at very low temperature a localized fermion system (i.e. a Mott insulator or solid He3) with spin degeneracy may exhibit a higher (spin entropy) than the Fermi liquid at the same temperature. Using a combination of thermodynamic identities and a Maxwell relation, the peculiar temperature dependence of the double occupancy can be related to interactioninduced adiabatic cooling. Since ultracold atoms are isolated systems, the relevant quantity is the entropy rather than the temperature and dynamic processes are naturally adiabatic. So when changing the interactions (adiabatically), cooling may occur as a result of the Pomeranchuk effect.
References

F. Werner et al., "InteractionInduced Adiabatic Cooling and Antiferromagnetism of Cold Fermions in Optical Lattices" , Phys. Rev. Lett. 95, 056401 (2005).

Z. Zhou et al., "Quantum Monte Carlo simulations of thermodynamic properties of SU(2N) ultracold fermions in optical lattices", Phys. Rev. B 90, 235139 (2014).

Robert C. Richardson, "The Pomeranchuk Effect", Nobel Lecture (1996).