Tidal forces are the driving factor for maintaining a liquid core. Europa, Io, Earth, Titan, and now Mercury illustrate this. Mars is larger and closer to the sun than all these moons, but has no tidal forces.
1. Our own moon violates this rule (it should be heated by the tidal force of the earth). When all is said and done I think we'll find that the moon's core is, if not molten, certainly heated.
2. Venus has a liquid core I believe, and it has no companion, no tidal forces.
Yes, I realize these statements contradict. Just throwing them out for discussion.