Add ice cubes to a sandwich baggie and hold the baggie on the plastic for two to five minutes until the burnt plastic hardens and becomes brittle.
Use a window scraper that features a razor blade attachment to carefully scrape the burnt plastic off the ceramic surface.
Scrape the plastic in a gentle manner with light pressure to prevent damaging the ceramic surface. If you meet resistance, hold the baggie filled with ice cubes for several more minutes and continue scraping until you have removed the burnt plastic.
Apply a thin layer of baking soda over one side of a damp sponge. Scrub the ceramic clean with the baking soda-covered sponge.
Wipe the gritty baking soda residue off the ceramic with a lint-free cloth and dry with a towel.