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The average density of fermions $\\rho_N(x,T)$ at position $x$ is derived. For $N \\gg 1$ and $\\beta \\sim {\\cal O}(1/N)$, $\\rho_N(x,T)$ is given by a scaling function interpolating between a Gaussian at high temperature, for $\\beta \\ll 1/N$, and the Wigner semi-circle law at low temperature, for $\\beta \\gg N^{-1}$. 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