Lol....been there done that. Not in our 319 but at home. Wife bought the cork protectors or hot pan pads as soon as we picked up our 319. Heres a link to some good info. I used the mayonnaise method here at the house and it worked.
Same with ours and they were plates that really were not that hot. We will strip it and put a proper finish on it. Then if that doesn't work out we will replace it with a solid surface of some sort.
Ours looks like its just a piece of plywood with that board pattern on it with an ebony stain or paint on it. Maybe try an ebony stain to go over it with lightly?