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 then it would cool. A light beam (radiant energy) pointed at the atmosphere might work.