[en] We study theoretically the magnetic Kapitza conductance at the interface between superfluid liquid ³He (in its A and B phases) and paramagnetic substances when the heat transfer across the interface is mostly due to magnetic couplings (either of contact or dipolar type) between the nuclear spins of ³He and the electronic spins of the paramagnetic substance. We predict that very close to the transition temperature the value of the Kapitza conductance should be higher when ³He is in one of its superfluid phases than it would be if ³He could remain in its normal phase at the same temperature; on the other hand at lower temperatures the Kapitza-conductance value drops sharply compared to what it would be in a normal rate at the same temperature