Cynthia - This is actually more of a chemistry question than a physics question, because it has to do with the chemical reaction that the plastic goes through when exposed to heat. Heat shrink tubing is made up of plastic that is only partially polymerized.
Heat is what's necessary to complete the chemical reaction.
You can think of it as if the plastic is only part-way formed before exposed to the heat. As the seperate monomers in the plastic are polymerized, they get closer together, making the plastic denser, which causes the tube to shrink. But because the polymerization reaction is one-way, the tube won't expand again once it cools down.