Pure metals like copper will not harden with heat like some alloys can. Sterling silver for example will harden some when heat is applied because of precipitates that come out of solution at elevated temperatures. The precipitates are new smaller crystals that grow in the grain boundaries of the existing crystal matrix. These stress the matrix and make the alloy harder. A pure metal has nothing in solution to precipitate so it will not harden in this way.
Any heat you apply to copper will just contribute to making it softer.
There is a phenomenon where pure copper and other metals will gain some hardness from heat. High temperature soaks for extended periods will first anneal the metal, but after a while the grain growth becomes very pronounced and there is a small jump in hardness. Its not enough to make a useful difference in your parts as its only slightly harder than a full anneal. The neat thing about it is the strange metallic fracturing noise that you can hear and feel when you bend the metal. Larger grains are breaking down into small units again and its so violent that you can hear and feel the tiny little shockwaves.
You can harden by mechanical means like peening, tumbling in steel shot, or vibratory finishing. these leave the surface hardened.
Not much you can do to a finished piece with out affecting the surface finish though.
patrick
