  We address a particular instance where open quantum systems may be used as
quantum probes for an emergent property of a complex system, as the temperature
of a thermal bath. The inherent fragility of the quantum probes against
decoherence is the key feature making the overall scheme very sensitive. The
specific setting examined here is that of quantum thermometry, which aims to
exploits decoherence as resource to estimate the temperature of a sample. We
focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic
regime (ranging from sub-Ohmic to super- Ohmic), by using pairs of qubits in
different initial states and interacting with different environments,
consisting either of a single thermal bath, or of two independent ones at the
same temperature. Our scheme involves pure dephasing of the probes, thus
avoiding energy exchange with the sample and the consequent perturbation of
temperature itself. We discuss the interplay between correlations among the
probes and correlations within the bath, and show that entanglement improves
thermometry at short times whereas, if the interaction time is not constrained,
coherence rather than entanglement, is the key resource in quantum thermometry.
