Hmm that's interesting, how does this system use energy to move heat around then, if there are no moving parts? Not a rhetorical question, I'm genuinely curious about this system, would you have more info or links to share?

Edit: I just saw the link from @Acters above, that's pretty cool. I'm not sure if it qualifies as "no moving parts" given that "Inside AirJet® are tiny membranes that vibrate at ultrasonic frequency", but I'm not gonna be hung up on a technicality, as it does seem a nice technology.

This is some company's page, but they have a pretty good demonstration of one common method

https://www.customchill.com/solid-state-cooling-systems/#:~:text=Solid%20state%20cooling%20systems%20have,of%20cooling%20or%20heating%20devices.