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Mercury's planet wide magnetic field is strongly suggests that the core of the planet must be at least partly molten, but there is no geological activity on the planet. The Magnetic field is weak but the planet turns more slowly on its access in comparison to terrestrial planets such as Earth and Mars. The best explanation I’ve heard was that the portion of the core that remains molten may not be large enough to create geological activity and that the outer part of the core must be solidified trapping the heat inside the inner core. I don’t understand this as clearly as I would like to… I mean heat radiates outward… even if a larger part of the core solidified shouldn’t heat from the molten core melt the solidified part that’s supposed to be trapping the heat. I’ve been thinking that the thin crust might have some kind of effect on the core. Plus the rock in the crust must effected by the planets tempter. The planets day side is supper hot wile the side faceting away from the sun is extremely cold that has to have some kind of effect on the crust. And since the crust is so thin the heating and cooling of the day and night cycles must also effect the core as well, or at least I would think it should.

The explanation sounds logical, but I don’t understand the mechanics of it…

All objects are slowly imploding due to gravity, that's where a fairly significant part of any objects heat comes from, though as I understand it for Terrestrial planets to retain liquid cores for any appreciable portion of there life requires significant radioactives in the core as well. However for the Gas Giants, it seems that is plenty sufficient to drive all kinds of interesting activity, such as Jupiter's Red Spots and Saturn's Dragon Storm

As for Mercury, that's just going to require more information. We still haven't placed anything into orbit around Mercury (yet, see Messenger) which has prevented us from getting really accurate density/gravity measurements.

Hard to make good a hypothesis with a severe lack of concrete information.