There appears to be a significant flaw in the specification. Technically whilst the inverter is limited in size, they have not limited what the inverter is contained in, so a liquid nitrogen bath comes to mind. Doing so makes the inverter quite easy to achieve and the temperature would remain very low even excluding the affect of the liquid nitrogen beyond it's super conductivity enhancing ability. So they should require the inverter function in a room temperature environment.
This is really all about materials design and molecular engineering. Creating micro channel structures to conduct the electricity, interleaved between layers of high heat conductivity material. Of course doesn't matter if it is small if you use very expensive material to manufacture it, you end up defeating your own purpose, like fooling around with platinum.