Rick, I take both stainless and carbon steels down to 0.03" to 0.02" pre-hardening. Probably most are at .03". This is using a digitally controlled oven. If I were heating in a forge, I'd likely leave my edges a bit on the positive of .03" so I'd have room to remove any decarb/scale.
I've found that as long as my grinds are even, I normalize prior to heat treating, and I go into the quench straight, I have had very little trouble with warping. This is with plate quenching steels (CPM154, 440C, ATS34), fast speed oil steels (W2, 1095, 1084), and medium speed oil steels (O-1). As I said before, if I were heat treating in a forge, I'd probably leave my edges thicker pre-HT.
Then again, maybe I've just been lucky

. I have had a few warp. One warped in the plates at the tip because I accidentally overlapped the folded foil over the tip. Another two were ground by another member. They were long, very thin (1/16" stock) O-1 kitchen blades. They both took very gentle warps. I had to stress relieve, straighten, and re-heat treat.
--nathan