My initial reaction is to say forget geat sealing without the right kit and use some glue.
If you are determined to have a crack at heat sealing it back together I guess you could try using a domestic iron. You might want to invest in an "El Cheapo" iron specifically for the job in case you get molten plastic all over the thing. Try running the iron along the bit you need to seal with the iron set on a low heat. If no effect, try again with it a little hotter etc etc until you find that you are indeed melting the layers together. I wouldn't keep the iron very still for long though