The trick is to heat up the plastic so it softens without burning. I used a "weather-proof" lighter which gives a hotter and cleaner flame. Note that I am heating the plastic with the jet of hot gasses from the flame rather than in the flame itself. If you are using a conventional lighter, then you'll want to hold the plastic above the lighter, and use the heat from the rising hot gasses (and I repeat: not the flame). As long as you don't burn the plastic, there won't be any burning plastic smell.
Be safe around fire and don't set fire to yourself, your things, or other people!