But copper is conductive, so it will conduct electricity too. This could possibly be placed in areas where copper can't be, maybe even much closer to (or even directly contacting) the actual copper traces in the chip.

Unfortunately I don't know enough about CPU manufacturing to speculate much more than that.

You're asking for a thermal jumper.

I don't know much about the inside of CPUs either. But I know that at the PCB-level, we use these devices to carry heat but not electricity.

https://www.vishay.com/en/product/60157/

Copper is still better at conducting heat. But just a little bit of thermal-jumper to make that small electrical separation is all you need.

Datasheet: https://www.vishay.com/docs/60157/thjp.pdf

In any case, modern material science provides us with plenty of useful insulators, conductors, thermal-conductors (but not electrical), semiconductors, and now semi-heat conductors (erm, thermal semiconductor?)

I don't expect the thermal semiconductor to be replacing any of the other materials we already use. Instead, we will find new discoveries and applications for things I can barely imagine.

If you want to conduct heat but not electricity, there's always diamond.

You're right, I forgot that diamond is very easy to grow on silicon during the CPU manufacturing process.

...this was sarcasm, just in case it wasn't already painfully obvious to the downvoters.

This requires a layer of gold below it, and a layer of graphene above it. If you’re worried about shorting things out, this isn’t your solution.

Oof. Good to know.