350F is way too low to temper a spring, assuming it was water quenched from red heat (about 1450-1600F) If the spring is too hard, say Rockwell C50, it will break one day just sitting in the lock.
Lots of quaint suggestions on how to temper a spring, in molten lead, until it reaches such & such color, etc., very interesting but they only work if you have started out with something not too hard. That is, maybe an oil quench for a 1095 spring might maybe work. OK, but water quench makes it too hard to deal with it easily, in a home shop.
There is a disconnect between what a metallurgist (yours truly) with accurate temperature control might do, and what one can actually do by eye. With a 1095 (high carbon steel, same as file steel) spring, given accurate temperature control, one would heat about 1450F and quench into salt water. Then reheat (temper) about 700 to 800F to get the right spring hardness, i.e., Rockwell C 40 to 45. That's great,
except 700F is too hot to judge by color, the temper colors have all faded out past pale blue by that time. Would take a Templestick, or more modern laser temperature measuring device. See your local welding supply shop.
Oil quenched 1095 does not get so hard to begin with, and might work tempered to blue, or just as the blue fades out.
Mediaeval guys heat treated armour with no good way to measure temperature. They did it in a manner to make a contemporary metallurgist cringe. That is, they heated the armour & then gave it what today we would call a "slack quench", that is, a lousey, too slow quench. So it wasn't all that hard coming out of the quench. And they could use it just as is. no reheat necessary.
by the way, soft or hard has nothing to do with how stiff a spring is. That is a hard concept to accept sometimes, but it is true. Stiff or weak comes from the design of the spring, how thick it is, mostly, and how wide open are tthe leaves.