Getting burned on plastic off a cooker hob

Whilst I was decorating we covered our ceramic hob with it's original wrappings - cardboard and bubble wrap. Unfortuately, (somebody who will be nameless!) managed to turn on one of the rings and after five minutes wondering where the burning smell was coming from found one ring covered in melted and charring plastic from the bubble wrap.
Could pick some big lumps off but quite a few plastic bits remain. It's cold now - anybody any ideas how to proceed now???
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