Possibly not the right solution for a Pyra, but recently a very flat vapor chamber cooling was announced:
Looks like Boyd already creates and sells them, but they are twice the thickness.
Seeing this https://liliputing.com/2021/12/raze...hones-and-android-phones-with-rgb-lights.html
got me thinking about GPIO access on the Pyra and it being similar to the Raspberry Pi in terms of software it can run...so: would we be able to rig up a Pimoroni fan shim to help cool the Pyra?
An external fan could probably applied more easy. Like the phone fan you've shown, there are generic ones that are really cheap and just use USB: https://www.aliexpress.com/i/4001134535835.html
Not sure how effective it is to just blow air against a case though, probably there are already tests available to show the effectiveness of phone-coolers but I don't appear to be able to find them.