The center is thought to be solid. It consists of iron and about 10% lighter elements, probably mostly nickel.

There is even a paper that states it is crystallizing at a rate of about 1 mm/year, and this process contributes some of the heat. [1] I have been trying to dig back to the data on this in the past, but haven't found anything but the claim itself.

[1] http://www.nature.com/ngeo/journal/v4/n4/abs/ngeo1083.html