Things are not the same for all kinds of planets. A rocky planet the size of Mercury is going to cool off much faster than one the size of Earth. This is largely due to the difference in volume to surface area ratios and related effects. A more massive planet will have a much higher amount of heat left over from formation, and it will lose that heat slower. Plus, it will have a higher quantity of radioactive elements relative to its surface area. This is why the Moon is geologically inactive while the Earth still is, despite being made of mostly the same stuff.

Once you scale up to gas giants these factors become even more important. Those planets retain a crap ton of heat from their initial formation and are comparatively inefficient at radiating it away into space. More so, they continue to generate heat through ongoing settling (raining of Helium down to lower levels of the atmosphere, for example).

That's not the case for Earth though, is it? I had thought it was the tremendous pressures that kept the internal core molten. If it was radiation wouldn't it be enough to destroy us living in such close proximity?

I am barely qualified to call myself even an amateur astronomer, so sorry if I've misinterpreted anything.

edit: re-reading the passage, it sounds like it's a combination of both (bottom of p.245, 246).

> If it was radiation wouldn't it be enough to destroy us living in such close proximity?

Different kinds of radiation differ by how deep they penetrate matter. Simplifying a bit you can imagine that for every atom the radiation passes, there's a probability that it interacts / gets absorbed.

Radiation that passes thousands of kilometres of rock without interaction will have a rather low probability of interacting with a mere metre (or so) of human.