  The dimensionality of a thermometer is key in the design of quantum
thermometry schemes. In general, the phenomenology that is typical of
finite-dimensional quantum thermometry does not apply to infinite dimensional
ones. We analyse the dynamical and metrological features of non-equilibrium
Gaussian Quantum Thermometers: on one hand, we highlight how quantum
entanglement can enhance the readiness of composite Gaussian thermometers; on
the other hand, we show that non-equilibrium conditions do not guarantee the
best sensitivities in temperature estimation, thus suggesting the reassessment
of the working principles of quantum thermometry.
