Just pay attention! If the spring is stiff, tempering is not gonna make less stiff.
Stiffness is only a function of the thickness. If you over temper the spring it won't return true, but take a new lazier set.
You need to temper just enough to push the break point to usable working range, but to be effective the spring needs to be able to return to true, otherwise the action will become sloppy with time.
Cheers
Stefano