  Recently, a cooling scheme for ultracold atoms in a bilayer optical lattice
has been proposed [A. Kantian et al., arXiv:1609.03579]. In their scheme, the
energy offset between the two layers is increased dynamically such that the
entropy of one layer is transferred to the other layer. Using the
full-Hilbert-space approach, we compute cooling dynamics subjected to the
scheme in order to show that their scheme fails to cool down two-component
fermions. We develop an alternative cooling scheme for two-component fermions,
in which the spin-exchange interaction of one layer is significantly reduced.
Using both full-Hilbert-space and matrix-product-state approaches, we find that
our scheme can decrease the temperature of the other layer by roughly half.
