Sort of inverse of burning out a handle?    I've forged using campfires and localized heat using how the fire was arranged. or even using a Bellows Stone technique.  Just tossing it in won't work.

When you go to weld it up; don't forget to preheat and post cool, I'd do each side separately to maintain the alignment if possible.

Mr. Cleave,

You do not have to earn your wife's good graces.

Toaster ovens are plentiful at your local thrift store. And they are not very expensive. Buy one and use only for heat treating.

(I suggest that you try them out,   in the store,  before purchase).

Have you considered placing most of the axe head in a water bath and heat treating just the sharpened end with a torch?

(a propane torch is sufficient).

SLAG.

 

Good for you! A great learning project. 

Follow Thomas advice. Just heat treat the edge. Bring about 1-1/2" to critical, then quench about an inch or so in water. Move the axe up and down a bit till cool. Quickly sand/file  the bottom ~ 3/4" inch and watch the colors run. Control with water and propane torch to get an even temper line/ area about a half inch or so from the edge. I'd run it to a dark straw. 

Thanks all for the advice. I'd much rather make mistakes on something like this than on something I'd lovingly pounded into shape for 3 days straight...