  Centres of galaxy clusters must be efficiently reheated to avoid a cooling
catastrophe. One potential reheating mechanism is anisotropic thermal
conduction, which could transport thermal energy from intermediate radii to the
cluster center. However, if fields are not re-randomised, anisotropic thermal
conduction drives the heat buoyancy instability (HBI) which reorients magnetic
field lines and shuts off radial heat fluxes. We revisit the efficiency of
thermal conduction under the influence of spin-driven AGN jets in idealised
magneto-hydrodynamical simulations with anisotropic thermal conduction. Despite
the black hole spin's ability to regularly re-orientate the jet so that the
jet-induced turbulence is driven in a quasi-isotropic fashion, the HBI remains
efficient outside the central 50 kpc of the cluster, where the reservoir of
heat is the largest. As a result, conduction plays no significant role in
regulating the cooling of the intra-cluster medium if central active galactic
nuclei are the sole source of turbulence. Whistler-wave driven saturation of
thermal conduction reduces the magnitude of the HBI but does not prevent it.
