The first thing I noticed is that by twisting the line until it self-coils into a tight spiral doesn't work very well, since the tight coil doesn't have much room to stretch out and retract like a spring. What I did was twist the line to the point just before it tries to coil up on itself and then wrap it around something to give the coil some diameter.
I used a hex key just because it was metal (so it wouldn't melt in the oven), had a nice diameter, and was within reach. I then used alligator clips to hold the line in place. I then annealed it in the oven at around 360 F for 30 minutes.
Check out the video to see it in action (sorry about the noisy hair dryer)