Re: How can I make an ice insulator for an ice cube about the size of a cup?

You need to minimize conduction and convection around the ice. Styrofoam (the 
white expanded plastic that hot drink cups are made of) is easily available and 
a pretty good insulator. Seal the ice block in a plastic bag and wrap as much 
styrofoam around all sides as you can, minimizing air spaces. When you run out 
of styrofoam, wrap a layer of aluminum foil and continue wrapping with crushed 
paper or cloth, perhaps alternating with aluminum foil.

Good luck.
David Winsemius.