  The precise measurement of low temperatures is a challenging, important and
fundamental task for quantum science. In particular, in-situ thermometry is
highly desirable for cold atomic systems due to their potential for quantum
simulation. Here we demonstrate that the temperature of a non-interacting Fermi
gas can be accurately inferred from the non-equilibrium dynamics of impurities
immersed within it, using an interferometric protocol and established
experimental methods. Adopting tools from the theory of quantum parameter
estimation, we show that our proposed scheme achieves optimal precision in the
relevant temperature regime for degenerate Fermi gases in current experiments.
We also discover an intriguing trade-off between measurement time and
thermometric precision that is controlled by the impurity-gas coupling, with
weak coupling leading to the greatest sensitivities. This is explained as a
consequence of the slow decoherence associated with the onset of the Anderson
orthogonality catastrophe, which dominates the gas dynamics following its local
interaction with the immersed impurity.
