I think you have it backwards
Heat has to be radiated away before any material can deposit onto the solid core from the liquid core-mantle boundary. Heat has to be released first, before contraction occurs, not the other way around. Generally, this is true when talking about a simple phase change from liquid to solid. But with the Earth's mantle, there is also radioactivity that generates heat. As such, it might remain hot and liquid for much longer than one might expect a non-radioactive liquid to remain hot, if judging solely based on heat capacity of the material. Is there a reference to the paper?
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