An ice cube would transfer heat to another object whose temperature is lower than zero°C (32°F).
A block of "dry ice" is sitting there at a temperature of -78°C (-109°F). An ice cube helps to melt dry ice nice and fast.
If you could find a block of solid nitrogen, its temperature would be 63K (-210°C, -346°F). An ice cube would transfer heat to that baby so fast that it would instantly boil.
