How do you refinish a Corian countertop?
Some serious buffing is required.  Not just of the burn area.. but you'll need to buff the nearby surrounding areas as well.

Two options:


do it yourself cautious: experiment with automobile "rubbing compound" on it.. if it works on a small area, expand to the entire area.
do it yourself confident: sand with 800 to 1000 grit sand paper.. if it works on a small area, expand to the entire area.
hire someone: a corian professional


I do #3 in good times, #2 in bad.  Good luck.