Ironing would seem to be preferred as you are actually pressing it flat, but the heat gun with a squeegee of some sort (not plastic!) also sounds like a way to go. Just sometimes my boxes are huge taking more than one 8 1/2 x 11" sheet (multiples are cut and pasted together).I've done exactly as you described. My clear coating is a lamination pocket, one side removed, and ironed* on. Works great. Haven't tried it on a plastic box though.
*EDIT: I also remember using a heat gun. I can't remember which is the right way to go.