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We consider the problem of estimating the temperature $ T $ of a very coldequilibrium sample. The temperature estimates are drawn from measurementsperformed on a quantum probe strongly coupled to it. We model this scenario byresorting to the canonical Caldeira-Leggett Hamiltonian and find analyticallythe exact stationary state of the probe for arbitrary coupling strength. Ingeneral, the probe does not reach thermal equilibrium with the sample, due totheir non-perturbative interaction. We argue that this is advantageous for lowtemperature thermometry, as we show in our model that: (i) The thermometricprecision at low $ T $ can be significantly enhanced by strengthening theprobe-sampling coupling, (ii) the variance of a suitable quadrature of ourBrownian thermometer can yield temperature estimates with nearly minimalstatistical uncertainty, and (iii) the spectral density of the probe-samplecoupling may be engineered to further improve thermometric performance. Theseobservations may find applications in practical nanoscale thermometry at lowtemperatures---a regime which is particularly relevant to quantum technologies.

Low-temperature thermometry can be enhanced by strong coupling