So it's hard to imagine biological life (chemical life?) without water or carbon, since they're such good solvents and building blocks, but we can at least imagine electronic or mechanical life which don't require them.

But what you can't get away from is heat dissipation.

Any life will use energy will generate heat will need to dissipate heat to maintain homeostasis.

Could you dissipate enough heat to exist at <10K, to maintain a technological civilization? Or would you be reduced to supercooling your entire environment?

Are there naturally occurring pools of liquid helium out there in the universe, maintained by natural processes, or are you left with vacuum relying on radiative cooling?