My corian counter top was damaged by heat. The spot is approx. 2 x 3 x 1/64 inches. How can I repair it without making an obvious spat? Thank you for advice.

Call an expert and they can fix it quickly and simply. Without the right tools it is likely that you could actually make it worse.

Corian can be sanded. You'd start with a fairly coarse paper for Corian, about 220. Sand just until you start to see the damage almost gone and then switch to a finer paper like 440. When the entire area is gone move to 800 and the wet sand with automotive black paper 1000 or finer. The last step would be to machine buff with rubbing compound. If you are not venturesome then go with a pro.

Corain is the same material and color all the way through. If the burn is only 1/64 deep you should be able to sand it out.