Feedback from AGN jets has been proposed to counteract the catastrophic cooling in many galaxy clusters. However, it is still unclear which physical processes are acting to couple the energy from the bi-directional jets to the ICM. We study the long-term evolution of rising bubbles that were inflated by AGN jets using MHD simulations. In the wake of the rising bubbles, a significant amount of low-entropy gas is brought into contact with the hot cluster gas. We assess the energy budget of the uplifted gas and find it comparable to the total energy injected by the jets. Although our simulation does not include explicit thermal conduction, we find that, for reasonable assumptions about the conduction coefficient, the rate is fast enough that much of the uplifted gas may be thermalized before it sinks back to the core. Thus, we propose that the AGN can act like a heat pump to move low-entropy gas from the cluster core to the heat reservoir and will be able to heat the inner cluster more efficiently than would be possible by direct energy transfer from jets alone. We show that the maximum efficiency of this mechanism, i.e. the ratio between the conductive thermal energy and the work needed to lift the gas, $xi_{mathrm{max}}$ can exceed 100 per cent. While $xi$ < $xi_{mathrm{max}}$ in realistic scenarios, AGN-induced thermal conduction has the potential to significantly increase the efficiency with which AGN can heat cool-core clusters and transform the bursty AGN activities into a smoother and enduring heating process.
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