As discussed in my previous post, temperature may be associated with how energy is distributed among microscopic degrees of freedom (like the vibrational motion of atoms in a solid, or how electrons in a metal are placed into the allowed electronic energy levels). Moreover, it takes time for energy to be transferred (via "inelastic" processes) among and between the microscopic degrees of freedom, and during that time electrons can actually move pretty far, on the nano scale of things. This means that if energy is pumped into the microscopic degrees of freedom somehow, it is possible to drive those vibrations and electronic distributions way out of their thermal equilibrium configurations.
So, how can you tell if you've done that? With macroscopic objects, you can think about still describing the nonequilibrium situation with an effective temperature, and measuring that temperature with a thermometer. For example, when cooking a pot roast in the oven (this example has a special place in the hearts of many Stanford graduate physics alumni), the roast is out of thermal equilibrium but in an approximate steady state. The outside of the roast may be brown, crisp, and at 350 F, while the inside of the pot roast may be pink, rare, and 135 F. You could find these effective temperatures (effective because strictly speaking temperature is an equilibrium parameter) by sticking a probe thermometer at different points on the roast, and as long as the thermometer is small (little heat capacity compared to the roast), you can measure the temperature distribution.
What about nanoscale systems? How can you look at the effective temperature or how the energy is distributed in microscopic degrees of freedom, since you can't stick in a thermometer? For electrons, one approach is to use tunneling (see here and here), which is a topic for another time. In our newest paper, we use a different technique, Raman spectroscopy.
In Raman, incoming light hits a system under study, and comes out with either less energy than it had before (Stokes process, dumping energy into the system) or more energy than it had before (anti-Stokes process, taking energy out of the system). By comparing how much anti-Stokes Raman you get vs. how much Stokes, you can back out info about how much energy was already in the system, and therefore an effective temperature (if that's how you want to describe the energy distribution). You can imagine doing this while pushing current through a nanosystem, and watching how things heat up. This has been done with the vibrational modes of nanotubes and graphene, as well as large ensembles of molecules. In our case, through cool optical antenna physics, we are able to do Raman spectroscopy on nanoscale junctions, ideally involving one or two molecules. We see that sometimes the energy input to molecular vibrations from the Raman process itself is enough to drive some of those vibrations very hard, up to enormous effective temperatures. Further, we can clearly see vibrations get driven as current is ramped up through the junction, and we also see evidence (from Raman scattering off the electrons in the metal) that the electrons themselves can get warm at high current densities. This is about as close as one can get to interrogating the energy distributions at the single nanometer scale in an electrically active junction, and that kind of information is important if we are worried about how dissipation happens in nanoelectronic systems.