We simulate the evolution of dense-cool clumps embedded in the intracluster medium (ICM) of cooling flow clusters of galaxies in response to multiple jet-activity cycles, and find that the main heating process of the clumps is mixing with the hot shocked jets' gas, the bubbles, while shocks have a limited role. We use the PLUTO hydrodynamical code in two dimensions with imposed axisymmetry, to follow the thermal evolution of the clumps. We find that the inflation process of hot bubbles, which appear as X-ray deficient cavities in observations, is accompanied by complicated induced vortices inside and around the bubbles. The vorticity induces efficient mixing of the hot bubbles' gas with the ICM and cool clumps, resulting in a substantial increase of the temperature and entropy of the clumps. For the parameters used by us, heating by shocks barely competes with radiative cooling, even after 25 consecutive shocks excited during 0.5 Gyr of simulation. Some clumps are shaped to filamentary structure that can turn to observed optical filaments. We find that not all clumps are heated. Those that cool to very low temperatures will fall in and feed the central supermassive black hole, hence closing the feedback cycle in what is termed the cold feedback mechanism.