  Using finite temperature strong coupling expansions for the SU(N) Hubbard
Model, we calculate the thermodynamic properties of the model in the
infinite-$U$ limit for arbitrary density $0\leq \rho \leq 1$ and all $N$. We
express the ferromagnetic susceptibility of the model as a Curie term plus a
$\Delta \chi$, an excess susceptibility above the Curie-behavior. We show that,
on a bipartite lattice, graph by graph the contributions to $\Delta \chi$ are
non-negative in the limit that the hole density $\delta=1-\rho$ goes to zero.
By summing the contributions from all graphs consisting of closed loops we find
that the low hole-density ferromagnetic susceptibility diverges exponentially
as $\exp{\Delta /T}$ as $T \to 0$ in two and higher dimensions. This
demonstrates that Nagaoka-Thouless ferromagnetic state exists as a
thermodynamic state of matter at low enough density of holes and sufficiently
low temperatures. The constant $\Delta$ scales with the SU(N) parameter $N$ as
$1/N$ implying that ferromagnetism is gradually weakened with increasing $N$ as
the characteristic temperature scale for ferromagnetic order goes down.
