Surely smiths – a smithy is where a smith works isn’t it?
Re your axe, well it depends. Some things are case hardened which means the outside is harder than the inside so it’s less brittle. You may have ground away the hard bit.
But generally, to temper things, you first need to quench them. This means heating it up to bright red hot then dunking it in WATER not oil (oil would probably result in an explosion). This makes it brittle and hard, with lots of small crystals in it.
Then you clean it up shiny and warm it until you see colours forming. What actually happens is the heat creates a layer of oxide, the thickness of which determines the colour it appears. A rough and ready technique for home metallurgists is to judge the temper by the colour. Darker reds and blues are harder but more brittle, lighter yellows and oranges are softer.
We used to have a guide on the wall of our metalwork shop in school showing the colours for applications – IIRC things you use to hit other things were yellow or orange, so they don’t shatter.
But don’t take my word for it 🙂 I think that’s very vague.. I’ve done this for small items I’ve made and it works, but you will need to do some more reading.
http://www.iforgeiron.com/topic/19867-how-to-heat-treat-this-axe/