there's no proof the heat can be utilized efficiently
Yes. It is basics of physics.
other than heating the facility in winter
and this is not "work" in terms of "proof-of-work"
Also even if the heat is 100% efficiently utilized
Perpetuum Mobile?

Again? Oh, no!
Bullshit, the energy being there doesn't mean it can be easily 100% efficiently utilized. Try convert sunlight into electricity with 100% efficiency? or build a simple household boiler with 100% efficiency?
In terms of heating the facility, it's usually a facility that doesn't need heating, most likely it needs cooling. Also it works only in winter.