Yeah, just inject lots of thorium and/or uranium into the core until it starts heating up...
I will assume you are being sarcastic here. Warming the core is pure science fiction IMHO.
By comparison, warming Mars would be relatively easy. Just manufacture large amounts of CFC's and emit them into the atmosphere. They are very strong greenhouse gasses and are relatively persistent, though they won't last forever. Emit enough of these and you may warm Mars up enough to release the frozen CO2 in the ground, which will lead to even more warming. Eventually you may be able to melt the frozen water, which will make life possible.
That isn't to say that this would be easy. You would have to mine fluorine and chlorine and then use a factory to make the gas. But it isn't that difficult. And even with Mars' lack of magnetic field, any atmospheric densification will likely last for millions of years. The MAVEN satellite will give us more reliable information on this.