Experiments are described on the power dependence of the Kapitza conductance of copper at temperatures between 1 and 2 K. It is shown that the effects found earlier by Cheeke et al. are much enhanced on clean copper surfaces. New transient effects with long delay times up to lO00 sec are reported. It is confirmed that the origin of the anomalous Kapitza conductance is situated in the layer of superfluid helium next to the interface. A model for the steady state effect is proposed in terms of localized heat transfer.

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