Box body of a commercial vehicle, - wherein the box body having a roof, having two longitudinal side walls (6, 7) supporting the roof and extending in the longitudinal direction of the box body, having an end wall connecting the longitudinal side walls (6, 7) in an end face region of the box body and having a rear wall connecting the longitudinal side walls (6, 7) on a rear side region of the box body defines a loading space, - wherein a transport cooling unit is provided on the box body which blows tempered air into the loading space via at least one discharge opening, - wherein, on the underside of the roof assigned to the loading space is provided at least one air duct (18, 19, 20), which extends along the roof and is formed by a sleeve element, which is held on the roof and has an entry opening (21, 22, 23) assigned to the discharge opening of the transport cooling unit as well as an exit opening (25, 26, 27) formed on the other end of the respective air duct (18, 19, 20), and - wherein between the discharge opening and the entry openings (21, 22, 23) of the air ducts (18, 19, 20) is provided an air supply device, which guides the tempered air flow discharged by the transport cooling unit through the discharge opening to one of the air ducts (18, 19, 20), by it comprising an inlet section (116, 116'), which sits on the discharge opening of the transport cooling unit and via which the tempered air flow discharged from the discharge opening enters into the air supply device, and comprising an adjusting section (119, 119'), on whose end facing away from the inlet section (116, 116') is formed an outlet section (120, 120') with a discharge opening, to which the entry opening (21, 22, 23) of the respective air duct (18, 19, 20) is connected, wherein the adjusting section (119, 119') is formed flexibly, articulatedly and/or telescopically in order to equalise an offset between the position of the entry opening (21, 22, 23) of the respective air duct (18, 19, 20) and the position of the discharge opening of the transport cooling unit such that after fastening the inlet section (116, 116') of the air supply device to the discharge opening of the transport cooling unit, the outlet section (120, 120') with its outlet opening can be guided to the entry opening (21, 22, 23) of the assigned air duct (18, 19, 20). - wherein the box body having a roof, having two longitudinal side walls (6, 7) supporting the roof and extending in the longitudinal direction of the box body, having an end wall connecting the longitudinal side walls (6, 7) in an end face region of the box body and having a rear wall connecting the longitudinal side walls (6, 7) on a rear side region of the box body defines a loading space, - wherein a transport cooling unit is provided on the box body which blows tempered air into the loading space via at least one discharge opening, - wherein, on the underside of the roof assigned to the loading space is provided at least one air duct (18, 19, 20), which extends along the roof and is formed by a sleeve element, which is held on the roof and has an entry opening (21, 22, 23) assigned to the discharge opening of the transport cooling unit as well as an exit opening (25, 26, 27) formed on the other end of the respective air duct (18, 19, 20), and - wherein between the discharge opening and the entry openings (21, 22, 23) of the air ducts (18, 19, 20) is provided an air supply device, which guides the tempered air flow discharged by the transport cooling unit through the discharge opening to one of the air ducts (18, 19, 20), by it comprising an inlet section (116, 116'), which sits on the discharge opening of the transport cooling unit and via which the tempered air flow discharged from the discharge opening enters into the air supply device, and comprising an adjusting section (119, 119'), on whose end facing away from the inlet section (116, 116') is formed an outlet section (120, 120') with a discharge opening, to which the entry opening (21, 22, 23) of the respective air duct (18, 19, 20) is connected, wherein the adjusting section (119, 119') is formed flexibly, articulatedly and/or telescopically in order to equalise an offset between the position of the entry opening (21, 22, 23) of the respective air duct (18, 19, 20) and the position of the discharge opening of the transport cooling unit such that after fastening the inlet section (116, 116') of the air supply device to the discharge opening of the transport cooling unit, the outlet section (120, 120') with its outlet opening can be guided to the entry opening (21, 22, 23) of the assigned air duct (18, 19, 20).