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.