Unfortunately, formica is a material that, as you know, will melt when it comes in contact w/heat. Other than possibly cutting out the 'bad area' (which would ential cutting out a rather LARGE area because of the placement of your seams), the only other novel idea I've got is that you cut the bad spot out and replace it with a decorative tile.
IF you want, you can buy yourself a tile that's large enough to use, say, as a hot plate. (The bigger the better so the heat doesn't 'sit over top' of the 'good' part of the countertop.) Anyways, go to your local Tile Retailer or Home Center and talk to them about the job. I would be easy to do if you take your time and use SHARP cutting tools. Use a good caulk that will take some heat. Other than that, I think you're left to a major repair.
IF you decide to go with a major repair, remember that the new part of the countertop may not 'match' exactly the 'old' countertop. My best to ya and hope this helps.