We were just having a discussion on multiple thermal cyclings to improve the grain.
I'm really not sure how much thermal stability plays into it but I DO know wood (and coal) stoves so prolly a good idea.
An interesting read is how the Japanese swordmasters forge a Katana.
Their "forge" for the initial steel is literally melt ore in a trench in sand. More like a luau
So what did you use to get the steel up to quench temperature?