For a mixed Gaussian probe, the post-selected quantum Fisher information grows with temperature and can surpass the non-post-selected strategy, while the signal-to-noise improvement is bounded by weak-measurement validity.
How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100.Physical review letters, 60(14):1351, 1988
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Temperature-induced measurement sensitivity enhancement via imaginary weak values
For a mixed Gaussian probe, the post-selected quantum Fisher information grows with temperature and can surpass the non-post-selected strategy, while the signal-to-noise improvement is bounded by weak-measurement validity.