An apparatus for heat shrinking a film wrapping an object includes a housing having a heat treatment chamber, a transport device for supporting and moving the object through the heat treatment chamber. Steam, supplied from at least one supply is led to at least a first and a second fluid outlet device and directed at the transported object using one or more outlets. The fluid outlet devices are disposed on opposite sides of the transport device. According to the invention the apparatus and method further include generating a downward directed fluid flow in an area extending between the fluid outlet devices having a lower temperature than the steam supplied from the outlets. This results in improved sleeving results and higher efficiency.