A device intended to assist in the accurate and controlled shrinkage of thermo-shrinkable container-jacketing material. Said device producing at least an elevated temperature in a heated processing zone. Heat energy available in said heated processing zone primarily derived from a first heat source, preferably pressurized steam. Said first heat source steam exhibiting preferred characteristics related to the controlled shrinking of thermo-shrinkable materials. A second heat source, other than steam, acting in cooperative relationship with said first heat source steam, delaying the decay of one or more preferred characteristics of said first heat source steam. Said first heat source steam, urging said heat-shrinkable materials to shrink, substantially conforming to receiving containers in a preferred manner along one or more axis.