Quantum critical points (QCP) arise when two non-commuting terms in the Hamiltonian stabilize, in the ground state, large-scale quantum fluctuations between incompatible orders. At a QCP, quantum entanglement is stabilized at all length scales, a property intrinsically robust within the so-called quantum critical fan, an extended region of the finite-temperature phase diagram where the scaling behavior of fluctuations is governed by critical exponents of the QCP. However, revealing explicitly this exquisite quantum behavior, and the potential resource contained in large-scale quantum coherence, is very challenging. In this talk, I will present an approach, especially suited to large-scale systems at thermal equilibrium, to separate quantum (i.e. coherent) from thermal (incoherent) fluctuations of arbitrary observables. I will discuss the potential usefulness of states stabilized in the quantum critical fan for quantum metrology.