Heat and Electricity

If electricity is a gas, as Maxwell and Tesla would have agreed on, then it must also have a temperature. This is the temperature of a subatomic gas and is not the temperature that we would normally feel.
On the other hand, as it is in contact with matter that we do feel a temperature of, these two temperatures will most of the time be the same.
However, as the particles that make up electricity are vastly smaller than those of other forms of matter, their temperature can change very quickly.

As with all gasses, if we compress it, its temperature will go up and upon sudden expansion, its temperature will go down.
As discussed earlier, the pressure of electricity is related to the square of the voltage. So if we increase the voltage, we increase the temperature, but also, an increase in temperature can increase the voltage. So we see that there is a relation between thermal and electrical conductance, namely we can increase the potential either by adding charge or by increasing the temperature.

This looks like a fine theory, but do we have any experimental evidence to support it?

Well, it looks like we do. If we use an IR-thermometer we are actually measuring the spectrum of the emitted black body radiation. This is (almost) the same for every kind of material and so it seems to be related to something more fundamental than the atoms that it is made of. This could be the temperature that we are looking for.
If we measure the temperature of, or around a Tesla coil with an IR-thermometer we will notice a short-lasting peak when the coil is switched on and a short dip when it is switched off, exactly as we would expect based on this theory.