  The Nagaoka ($U=\infty$) limit of the Hubbard model on a square lattice is
mapped onto the itinerant-localized Kondo model at infinitely strong coupling.
Such a model is well suited to perform quantum Monte Carlo (QMC) simulations to
compute spin correlation functions. This model is shown to exhibit no
short-range ferromagnetic (FM) spin correlations at any doping $\delta\ge 0.01$
and finite temperature, $T=0.1t$. Our simulations give no indication that there
is a tendency towards ferromagnetic ordering in the ground state.
