  We investigate a species selective cooling process of a trapped
$\mathrm{SU}(N)$ Fermi gas using entropy redistribution during adiabatic
loading of an optical lattice. Using high-temperature expansion of the Hubbard
model, we show that when a subset $N_A < N$ of the single-atom levels
experiences a stronger trapping potential in a certain region of space, the
dimple, it leads to improvement in cooling as compared to a $\mathrm{SU}(N_A)$
Fermi gas only. We show that optimal performance is achieved when all atomic
levels experience the same potential outside the dimple and we quantify the
cooling for various $N_A$ by evaluating the dependence of the final entropy
densities and temperatures as functions of the initial entropy. Furthermore,
considering ${}^{87}{\rm Sr}$ and ${}^{173}{\rm Yb}$ for specificity, we
provide a quantitative discussion of how the state selective trapping can be
achieved with readily available experimental techniques.
