The ice cubes melt because they are absorbing heat from their warm surroundings.
One of the laws of Nature is that heat flows spontaneously from a warm object to a cooler object.
If you take an ice cube at 0 °C from its container and hold it in your hand or place it on a table top, it will be in warmer surroundings.
Your hand is at 37 °C, and the temperature of the table and the air may be between 15 °C and 40 °C.
The molecules in your hand and in the air have more heat energy than those in the ice.
Energy flows into the ice, and the water molecules gain enough energy to leave the surface of the ice. The ice melts even though you don't add extra heat.
At the South Pole, the ice cube won't melt, because the temperature is probably between -25 °C and -65 °C. You won't even need to keep the ice in a refrigerator.