An improved method for cleaning heat exchange tube bundles, fin-fans, and other elongated components, using a portable cleaning system comprising a cleaning unit having a cleaning enclosure that receives and cleans the component and a control unit that controls the operation of the system. The cleaning unit has a cleaning enclosure defining a chamber sized and configured to receive the component through a sealable lid. A roller assembly rotates the component while a spray assembly sprays cleaning fluid over and into the rotating component. The cleaning fluid is heated in the chamber using surface heating elements attached to heat transfer plates along sections of the chamber walls. A vapor recovery system captures and treats toxic vapors. In use, the cleaning system is transported to a facility to clean the components on-site using cleaning fluid supplied by the facility and discharging waste to the facility.