graveyard, with carbon steel in 1/8" thick stock, just try to grind equal amounts on both sides, as you go, and not getting the blade really hot while grinding, as getting it super hot will add stress in the blade and may cause warpage in the quench, and leave at least .040" thick at the edge before heat treat, around .060" won't hurt just more to grind after heat treat. I like to quench point down in the oil. 1/8" is not difficult to heat treat, unless maybe it is a really long blade. For stainless and air hardening carbon steels, do the same grinding practices, but quench between heavy aluminum plates.
Hope this helps. Dale