On my old 06 Ram I had some scratches on the glove box door and some on the door panels. I tried heat from a heat gun and it removed about 70% of the scratches. Be careful, you could warp or melt some pieces or even make shiny spots where it got to hot. I have also heard some people have used a hand held propane torch (Blue Bottle). I was afraid to try this method. Also, don't get the heat of flame to close the plastic until you get use to it. And yes, carpet will melt in a heart beat.
If you are going to do it as mentioned above, start with low heat first and watch what you are doing. Once you make a mistake, there is no going back.