  Probes that measure the local thermal properties of systems out of
equilibrium are emerging as new tools in the study of nanoscale systems. One
can then measure the temperature of a probe that is weakly coupled to a
bias-driven system. By tuning the probe temperature so that the expectation
value of some observable of the system is minimally perturbed, one obtains a
parameter that measures its degree of local statistical excitation, and hence
its local heating. However, one anticipates that different observables may lead
to different temperatures and thus different local heating expectations. We
propose an experimentally realizable protocol to measure such local
temperatures and apply it to bias-driven quantum dots. By means of a highly
accurate open quantum system approach, we show theoretically that the measured
temperature is quite insensitive both to the choice of observable and to the
probe-system coupling. In particular, even with observables that are distinct
both physically and in their degree of locality, such as the local magnetic
susceptibility of the quantum dot and the global spin-polarized current
measured at the leads, the resulting local temperatures are quantitatively
similar for quantum dots ranging from noninteracting to Kondo-correlated
regimes, and are close to those obtained with the traditional "local
equilibrium" definition.
