It doesn't say the the opening has to be a certain diameter does it? If not the take the cardboard make a second cup but 1 cm bigger(in diameter and dept), line the outside of the Styrofoam cup in aluminium, shinny side facing in. Put Styrofoam cup in the bigger cup and fill will foam chip.
If it must be practical and you must be able to drink out of it, the don't fill the gap with foam all the way up, bend the 2 edges together and tape.

Or the other way arround woul be better, cardbaord inside and styro cup out insde, but not quite sure how to make the coffe stay in carboard, unless lining the inside of that one with platstic wrap, then i would be just like a styrofoam cup but thicker!