  We analyze the Bures metric over the manifold of thermal density matrices for
systems featuring a zero temperature quantum phase transition. We show that the
quantum critical region can be characterized in terms of the temperature
scaling behavior of the metric tensor itself. Furthermore, the analysis of the
metric tensor when both temperature and an external field are varied, allows to
complement the understanding of the phase diagram including cross-over regions
which are not characterized by any singular behavior. These results provide a
further extension of the scope of the metric approach to quantum criticality.
