An insulated beverage or food container or sleeve is produced with a foam layer disposed on an inner surface of a paper stock. A polymer shrink film layer is arranged in a position along an inside surface of the beverage container. The foam layer is sandwiched between the polymer shrink film layer and the paper stock and decreases the energy transfer between the beverage and the user's hands allowing the user to hold onto the container for an extended period of time without causing user discomfort or pain. The polymer shrink film layer is produced from a shrink film polymer having a percent shrink in the range of 30% or less, and more particularly a percent shrink range of 5 to 10%.