Why would you a device with variable electrical conductivity? If you’re transmitting a signal you want a high electrical conductivity all the time…

What someone said when vacuum tubes were invented.

Why would you want a device with variable thermal conductivity?

Because not all electronics are the same

Especially for high precision analog circuitry either a lot of effort is put into either making it temperature insensitive or stabilising the temperature of the critical components

under normal conditions.

Under normal conditions there isn’t much importance, as cooling to room temperature isn’t really a problem. Under abormal conditions you have a few more options for thermal management. Assuming this process has no vibrations or detracting factors, and doesn’t consume more energy for heating, I can think of situations where this may be useful. Neither application is really consumer facing, and more under the commerical side of things.

First one, would be scientific equipment that is temperature sensitive for measuring vibration in a range of extreme enviroments.

Second one - and one I think is much more compelling - would be satellites. Temperature management, and just maintaining component health, is a pretty big deal when it comes to continued operation when you can have a potential 200C temperature differential from the outside of the lit surface to the dark side of the other. Being able to retain heat better as opposed to having to engage electric heating elements during periods of low power use/thermal generation from onboard systems, would be a great change.

But can a chunk of metal modulate its thermal conductivity?