  When quantum information is spread over a system through nonclassical
correlation, it makes retrieving information by local measurements
difficult---making global measurement necessary for optimal parameter
estimation. In this paper, we consider temperature estimation of a system in a
Gibbs state and quantify the separation between the estimation performance of
the global optimal measurement scheme and a greedy local measurement scheme by
diagonal quantum discord. In a greedy local scheme, instead of global
measurements, one performs sequential local measurement on subsystems, which is
potentially enhanced by feed-forward communication. We show that, for
finite-dimensional systems, diagonal discord quantifies the difference in the
quantum Fisher information quantifying the precision limits for temperature
estimation of these two schemes, and we analytically obtain the relation in the
high-temperature limit. We further verify this result by employing the examples
of spins with Heisenberg's interaction.
