  The entropy-temperature curves are calculated for non-interacting fermions in
a 3D optical lattice. These curves facilitate understanding of how adiabatic
changes in the lattice depth affect the temperature, and we demonstrate regimes
where the atomic sample can be significantly heated or cooled. When the Fermi
energy of the system is near the location of a band gap the cooling regimes
disappear for all temperatures and the system can only be heated by lattice
loading. For samples with greater than one fermion per site we find that
lattice loading can lead to a large increase in the degeneracy of the system.
We study the scaling properties of the system in the degenerate regimes and
assess the effects of non-adiabatic loading.
