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Cannot radiate cold. Can have a cool surface that absorbs radiation.

If you are consuming energy you are producing heat unless it is performing other work like lift a rock.

Yes you could cool a large object with high heat capacity but you would produce more heat cooling it then the object will absorb. If you could cool the object in space it would work.

A refrigerator in net produces heat but if you could get that heat out of the atmosphere than it would cool. A light beam (radiant energy) pointed at the atmosphere might work.