what kind of stain? does it say flammable or toxic on the container?
If the limbs are only 3/16 thick and you've used a penetrating stain, then my impression is that you should give up the idea of heat treating it, and just make a new bow. Also, if you do decide to heat treat it, heat the belly, not the back. Go to Marc St. Louis' website, he has a tutorial on heat treating. You can find it by going to the members list, finding him, and clicking on the link.