Using power to generate work is not what happens in air conditioning. With air conditioning, you are moving heat from one spot to another (another word for it: "heat pump"). That is why it's over 100% efficient.
Generating economic value from work that the OP describes would not be "air conditioning" it would be converting heat into work -- which cannot be over 100% efficient, and in fact would be significantly less than 100% efficient at the temperatures we know.
Removing that heat using a heat pump would require some off-world reservoir of cold, which doesn't exist. The reservoir of cold that we are using now (and in any conceivable future) is the earth itself, which is what the parent comment means by "you can't use the work."
It is. We receive light from the sun in the visible light range. Earth emits something like 20 photons in the infrared for each incoming visible light photon. The reason is that the sun’s surface temperature is ~20x higher than Earth’s.
Generating economic value from work that the OP describes would not be "air conditioning" it would be converting heat into work -- which cannot be over 100% efficient, and in fact would be significantly less than 100% efficient at the temperatures we know.
Removing that heat using a heat pump would require some off-world reservoir of cold, which doesn't exist. The reservoir of cold that we are using now (and in any conceivable future) is the earth itself, which is what the parent comment means by "you can't use the work."