I noticed that after shaving my wheels it was very easy to melt them when polishing them. I had polished a couple of "practice" wheels just before polishing my "perfect" shaved wheels I was going to use on our car. The practice wheels came out better then ever before due to using the super ultra fine paper. I used to stop at 1500 or 2000g then polishing compound and graphite. They gleamed like new gun metal! I was more then satisfied with my polishing technique and regimen. I put on the good wheels that I had shaved darn near perfect round and they started to melt and became unworkable. I did not apply much pressure, lighter then the practice wheels successfully done not minutes before ruining the good wheels. I grabbed another spare practice wheels and it shined up perfect.
You don't want the tread surface to be so slick it slides instead of rolling this will cause wobbles. Graphite on the tread surface is not the way to go, it makes the wheels shine but it also slows the car down, use a good plastic polish with light pressure at slow speeds or by hand. If your melting wheels then your turning them to fast. IMO
I am new to pinewood derby but I know many run graphite treated wheels on the treads. When I do radio control 1/5 racing spray my wheels with WD40 because it softens the rubber which I understand that is totally different. The reason I am getting in to pinewood derby is my grandson and he has 3 bothers so I am sure I am going to get a lot of experience. LOL