There are two main types of heat transfer, convection and conduction. You need to try to prevent both of those. Air by itself is a very poor conductor of heat. This means that it is a good insulator. But, it can allow a lot of convection. To prevent this, you need to isolate the air into small pockets (like a foam). The first thing that came to my mind that you would easily find around the house would be a sponge. If you surrounded your ice cube by a few sponges that would work well (hopefully you can find enough to line the walls). I bet that would do very well at insulating your ice cube. Good luck