Ice cube and pillow

We will need:
a pillow
few ice cubes
2 glasses

I’ll take ice cubes and I put them into the glasses. Now, I’ll give the pillow on the first glass with ice cubes.
We have to wait for 2 minutes.
After 2 minutes we can see how the ice cubes under the pillow melt down as slowly as ice cubes without a pillow. Why? The pillow doesn't heat, pillow keeps a body temperature. So, the pillow can't heat up ice cubes.