Mix one part vinegar with two parts cold water in a spray bottle. Shake the bottle well and spray the burn mark heavily with the mixture. Allow it to soak for five minutes, and then wipe it off. Allow it to air-dry.
Attach a piece of 100-grit sandpaper to the bottom of an electric sander. Run the electric sander around the surface area of the burn. This will help to buff out the burn mark and allow the Formica to accept the paint. Repeat this step with a piece of 220-grit sandpaper.
Dampen a soft cloth with mineral spirits and wipe away the dust from sanding.
Dip a painter's sponge into an oil-based primer and dot the burn mark area with primer. Allow it to dry for four hours. Apply a coat of laminate paint in a color that matches your counter, using the sponge with a light dabbing motion. Allow the paint to dry overnight.
Dip a 3-inch paint roller into a coat of clear polyurethane and cover the repaired area with a light coat. Give it 24 hours to dry.