I don't have much problem doing heat correction or tempering on bare wood, either, as long as the bends I'm attempting are reasonable. But oiling the wood seems to pull the heat in, get the heat distribution and color nice and even, and prevents me from burning it as much.
I have never bothered to try to get the oil out, and the only reason I can think of that I would is if I needed to glue something on or laminate it, and since I only do any heat correction on selfbows, I'ts never come up. It soaks in, cooks off, and the wood feels pretty dry and not greasy after the heating, it has never messed up staining or finishing, and it usually disappears with a little sanding or scraping anyway, right as I finish the bow.