  The interplay of quantum and thermal fluctuations in the vicinity of a
quantum critical point characterizes the physics of strongly correlated
systems. Here we investigate this interplay from a quantum information
perspective presenting the universal phase diagram of the quantum Fisher
information at a quantum phase transition. Different regions in the diagram are
identified by characteristic scaling laws of the quantum Fisher information
with respect to temperature. This feature has immediate consequences on the
thermal robustness of quantum coherence and multipartite entanglement. We
support the theoretical predictions with the analysis of paradigmatic spin
systems showing symmetry-breaking quantum phase transitions and free-fermion
models characterized by topological phases. In particular we show that
topological systems are characterized by the survival of large multipartite
entanglement, reaching the Heisenberg limit at finite temperature.
