Hammerite produces a range of specialist paints for painting / treating metals. AFAIK they don't produce paint suitable for timber.
Their paints bind chemically to metal, rust or metal paint and probably won't work with timber. You'll need to get the timber out as the paint wont be bound properly and is probably still inside the timber's fibers and is giving off fumes.
I'd suggest masonry or metal is the safest options for behind a stove.