If you have 1 gram of ice at zero degrees C, you have to pump 334 joules of heat energy into it in order to<em> just change it from solid to liquid</em> at the <em>same temperature. </em>
This is one of the highest figures known for any substance, and that's why a piece of ice does such a good job cooling your drink.
So basically the objects would be sandpaper and smooth metal, the sandpaper can indirectly touch the metal since it’s so smooth and it won’t cause any temp change either