To cool down electrons you can place them in a "fridge". Suppose you have a chip. TO cool down the electrons flowing in the chip transistors you can place the chip in liquid nitrogen and as the chips cools down so do the electrons flowing through it.
This approach does not work in practice, since the chip (and the device it is embedded in) can only operate at higher temperature- notice the warning on your cell phone package telling you that you must operate your device within certain temperature ranges, usually from a few degrees below zero to about 50 degrees above. This is not an operation constrain coming from the chip but from the screen and the battery. Nevertheless, it is not possibile to put our devices chip in a fridge and that's a pity since it would consume much less energy, 100 world less making your cell phone working form months rather than for hours.
Now researchers at Arlington University have found an ingenious way to cool electrons without resorting to a fridge!
For the technical details you should read their paper, and be prepared to dig into your quantum physics memories... Here I just try to outline the principle, for those who might have forgotten quantum physics, with a apologies to those who haven't.
What the researchers have managed to do is basically to filter the electrons at a lower level of energy (the coldest one) from those at higher level of energy (the hot ones). To do this they have created a filter that through a quantum well actually block hot electrons so that they are not involved in moving from one place of the chip t another (the signal is being carried by the electromagnetic spectrum not by electrons per se, although the vary fact that there is an electromagnetic field causes electrons to move, albeit at a much lower speed). You can see the schematics in the first figure.
By introducing this sieve in from of a transistor in a chip they can actually confine hot electrons and use only the cold ones reducing the power consumption and related heat dissipation. This will benefit batteries in the first place and processing as a second step (see the prototype chip in the second figure).
Both the physics involved and the manufacturing processes are quite complicated but the researchers expect that in a few years we might indeed have cold chips (and batteries) available. Another way to lengthened the Moore's law life.