IMO, heating the axle won't affect it significantly. After all, it was once red hot when it was forged. To be totally sure, the entire axle should be heated cooled evenly. But you probably don't have the facilities to heat the whole thing to the same temperature. The problem with heating the machined ends (kingpin holes) is that it will then need to be re-machined. I would be more concerned about the welding he did on the top flange near the spring perches, which would tend to shrink there and pull the axle out of alignment at the spring perches. Also the track on the axle he dropped was narrowed a fair amount. If you look at the video
www.youtube.com/watch?v=eGcG1oojZGU at about 19:40 you can see the axle shortening as he bends the second end.
I have to agree with Jerry on the cost of the setup to drop an axle. Just not worth it for a DIY on one axle.