The heating element (the black part) is connected to the silver part along the full length of the flexwatt, so warping it or melting it at the soldering point shouldn't have any effect on the rest of the strip. If it still isn't working right you can always cut off the section you already have soldered and try again, just be sure to put electrical tape over any point that the heating element is cut.

I actually cut the plastic off before even touching the soldering gun. I use a razor to make a cut on each side of the flexwatt about 1/4" in from the end up to the silver part, then cut across the plastic in the middle, leaving just the silver part sticking out with no plastic around it. Then the plastic left on the silver part itself will lift right up on one side and you can cut it off. I hope that made sense? I don't think I've got a spare piece of flexwatt laying around or I'd just take some pictures of the whole process.