We analyze three-dimensional hydrodynamical simulations of the interaction of jets and the bubbles they inflate with the intra-cluster medium (ICM), and show that the heating of the ICM by mixing hot bubble gas with the ICM operates over tens of millions of years, and hence can smooth the sporadic activity of the jets. The inflation process of hot bubbles by propagating jets forms many vortices, and these vortices mix the hot bubble gas with the ICM. The mixing, hence the heating of the ICM, starts immediately after the jets are launched, but continues for tens of millions of years. We suggest that the smoothing of the active galactic nucleus (AGN) sporadic activity by the long-lived vortices accounts for the recent finding of a gentle energy coupling between AGN heating and the ICM.