What is the cause of this adhesion?
I propose a slightly different hypothesis from ringo. As opposed to the very cold ice freezing water in the material, I would presume the material to initially be dry, but at room temperature. This room temperature material may melt the outer layers of ice molecules, both cooling and wetting the material.
Then as the temperature equalizes, and the material does not further conduct heat into the wet areas, the wet material becomes cold enough to freeze again, creating the sticky effect you ask about.
Why does the effect vanish after some time?
The temperature gradient is not static, and the material will conduct some heat through it, so the sharp gradient that caused the melted ice to freeze again becomes a gradual gradient that shifts towards the center of the ice, and the water that refroze so quickly melts again, and the sides of the ice are no longer cold enough to refreeze any bits of them that happen to melt by exposure to a new contact surface.