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The problem is set in an exterior two-dimensional domain which excludes a hole $\\mathcal{H}$, and with zero Dirichlet data on $\\mathcal{H}$. In the far field scale, $\\xi_1\\le |x|t^{-1/2}\\le \\xi_2$ with $\\xi_1,\\xi_2>0$, the scaled function $\\log t\\, u(x,t)$ behaves as a multiple of the fundamental solution for the local heat equation with a certain diffusivity determined by $J$. 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