No, No, No, No and No again. Especially high heat like a fire. Even an oven on cleaning cycle can damage or warp a vintage piece of iron. If you don't care about the piece do as you please.
If it is just crud and old cooking build up a lye tank. If it very , very light flash rust you may be able to use steel wool. Don't go too abrasive. No to any power tools. If rust is more of a problem build and electrolysis tank.
BilletHead