The sort of auger I'm envisioning you have probably won't be exotic steel, so a weld built up with high carbon steel rods would be adequate, [if they can be got?]. Ordinary MS rutile rods are not hardenable, you need about 0.85% carbon content.
Using hardfacing rods, [such as 14% manganese], presents the problem of reshaping the cutting edges after welding, but with the right wheel, it can be done.
No heat treatment required, these steels either self harden or workharden at room temperature.
With carbon steels, after welding, cut the new teeth with a grinder - no need to anneal the weldment- raise it to bright red heat then plunge in water to get it hard. Test with a file to see how you did- it should be unfileable.
Don't overheat it! If you 'burn' the steel [white hot with sparks] you have a turbo paint-stirrer - the metal is ruined and unredeemable.
Tempering reduces the hardness [ reduces tendency to brittle chipping] and increases toughness [ but increases the wear rate ] so you need to know where to stop. Clean off any crud and oxide back to bright metal, enough to see what's happening, and heat slowly from well up the shank of the auger and watch carefully as the colors approach the tip. Don't worry about the rest of the auger just watch the tip. As the tip goes yellow/brown quench in water. Overdo the tip tempering to blue and you are back to a soft steel again!
One thing- you need to get both cutting edges on the auger the same, or it will cut a larger hole or be unmanageable.
Distortion is easy to avoid- heat the auger slowly and evenly, and plunge in the water vertically, not on the slant. If you do bend it with heat, temper it right out to light blue or dull red, belt it straight with a hammer and have another go! You can repeat hard/temper operations a few dozen times without harm.
Best of luck!
Alan
