The idea behind using a woodstove is to stick it into a really hot fire and cook it. Wood stoves run much hotter than a regular fire. At the end of the day, you leave it in the coals to cool with them. As the fire and coals slowly die out, the steel cools slowly with them. The next day you take it out and try machining it.
It's not the best method but you use what you have access to. It may or may not work but you have nothing to lose. It has worked for me using torsion bars which are probably very similar.
Don't expect a beautiful finish.
The file test I thought you meant was the hardness test file set, not ordinary files.