All the NUCs and other mini PCs I see run mobile processors.
It’s a shame because a simple downdraft air cooler with a 120mm fan can handle a pretty high power load and could definitely fit in a tiny space.
Add a few thunderbolt ports and you could have a capable and upgradeable little pc.
You can always built a micro ITX real server with some of the AsRock server boards. Not as small as a NUC but pretty small considering their capabilities.