I've tuned all my pennywhistles (Generation) in the following manner:
First, heat up some water in a ceramic mug in the microwave, like you were making tea. It should be really hot but NOT boiling.
Then, submerge the entire plastic mouthpiece of the whistle in the mug. Let it
sit for a minute. Then try pulling the mouthpiece off. If it doesn't come off, heat up the water for a few more seconds in the microwave. Just make sure it isn't starting to boil. Soak mouthpiece some more.
When the mouthpiece comes off, wipe off as much of the glue residue as you can. Then coat the metal end with petroleum jelly. This makes the mouthpiece easier to slide around. Put the mouthpiece on and tune it up. The petroleum jelly seals it up pretty well when you've found the optimum spot for the mouthpiece.
As other posters have noted, not all inexpensive whistles are in tune with themselves. Some always have a note or two that are slightly "out".

I've never melted a plastic mouthpiece using this method. Good luck!   

Wyllow :)