  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.
