  Measuring local temperatures of open systems out of equilibrium is emerging
as a novel approach to study the local thermodynamic properties of nanosystems.
An operational protocol has been proposed to determine the local temperature by
coupling a probe to the system and then minimizing the perturbation to a
certain local observable of the probed system. In this paper, we first show
that such a local temperature is unique for a single quantum impurity and the
given local observable. We then extend this protocol to open systems consisting
of multiple quantum impurities by proposing a local minimal perturbation
condition (LMPC). The influence of quantum resonances on the local temperature
is elucidated by both analytic and numerical results. In particular, we
demonstrate that quantum resonances may give rise to strong oscillations of the
local temperature along a multiimpurity chain under a thermal bias.
