The easiest (and most enjoyable) way to harden 14g round copper is to forge it. Use a chasing hammer with a steel bench block or vise, or get a regular ball peen hammer (if it's been in the garage or basement for a while, use a grinding wheel or sandpaper to smooth both heads). The flat head, on either hammer, will flatten and slightly stretch the metal while hardening it, as well as adding a slight 'rise' to the piece (which you could incorporate into your desired shape) and the ball head can texture it. Experiment first, using a piece about 3 to 5 inches long, so you have enough to hold on to. (The scrap could later become a pair of earrings.) Forging/beating soft wire into different shapes can be a lot of fun!
The project on DVD #4 of the new Intermediate DVD series, introduces forging with a really cool Cuff Bracelet.
Answer contributed by Dale "Cougar" Armstrong