A working assembly (1) includes a rotatable hollow drum or cylinder (2) having a cylindrical wall (3) with ends having transverse header walls (4) with openings (16, 17), and with a longitudinal shaft (5). The external lateral surface of the cylindrical wall (3) has a clothing device intended to interact with the fibers being carded. First and second support uprights (6, 7) are fixed in operation, and adapted to support the ends of the shaft (5) of the drum or cylinder (2) for rotation about a preferably horizontal axis. The support uprights (6, 7) and the drum or cylinder (2) are configured and coupled with each other such as to define at least one fluid path for a flow of a refrigerating fluid, which extends through the openings (16, 17) and inside the drum or cylinder (2) and is adapted to cause cooling of the lateral cylindrical wall (3) thereof.