We study the thermodynamics of a single hole in the $U=\ensuremath{\infty}$ Hubbard model using a Monte Carlo method which samples graphs that contribute to the partition function; there are no finite-size effects. The heat capacity and magnetic susceptibility indicate a sharp transition between a high temperature spin-polaron and a compact ferromagnetic droplet at low temperature. When applied to trapped vacancies in solid $^{3}\mathrm{He}$, this transition would occur near 5 mK.