Thee is annealing, hardening and tempering. Three distinct processes. Yes, anneal the spring first. The re-shape it to whre you want it.
Then harden it by heating it to the proper temp and quenching it. Now it is "file-hard" but very brittle.
So you must now temper it by placing it at a known temp for a certain length of time.
The problem is, you don't know the spring alloy so you don't know if it is oil, water or air-hardening (I would guess it's oil)
And since you don't know the alloy you don't know the tempering requirements but you can do this by color rather easily if you have an electric oven.
When you watch someone experienced do it the process looks simple but in reality takes a lot of skill.
