Ice in blanket

When we take a blanket at room temperature and wrap it around ourselves, we become warmer than if we are not covered by the blanket.

When we take a blanket at room temperature and wrap it around an ice cube, would the ice melt faster or slower than if it was not covered by the blanket?

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Details and Assumptions:

• Assume that the ice does not touch the blanket due to an air gap between the blanket and the ice.
• The initial temperatures of the blanket and the room are the same.