I'm most of the way through reading Neil deGrasse Tyson's book "Origins", and I just finished chapter 24 last night, which deals with this exact subject.
By the way, it looks like the entire book is available online; this[1] is a link to the section of ch. 24 that talks about these star-less planets and the possibility that they contain life.
First, he points out the "extremophiles" that exist on earth -- for example, organisms that live on the sea floor, where the heat from the sun is fully nullified. Despite the great atmospheric pressure and the lack of light and heat, life still thrives in these environments. One of the factors that facilitate life at these extremes are the geothermal processes (vents in the sea floor) which are purely disconnected from the events of the sun, and completely powered by our magma core.
As we know, many planets are suspected to have molten cores, which are the result of their formation and which will continue to remain such for billions of years (we will probably be wiped out by our Sol turning into a red giant before our the Earth's core will lose it's energy). As such, though it'd be near-impossible for life to survive on the surface of a planet that is not a part of any solar system, under the surface life could be bountiful.
The core of planets do not remain hot for billions of years based on their formation. They remain hot because they have radioactive material that continues to generate heat.
Before the discovery of radioactivity invalidated the calculation, the fact that the Earth's interior is still hot was used by Lord Kelvin to set an upper limit of 40 million years for the Earth's age.
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.
By the way, it looks like the entire book is available online; this[1] is a link to the section of ch. 24 that talks about these star-less planets and the possibility that they contain life.
First, he points out the "extremophiles" that exist on earth -- for example, organisms that live on the sea floor, where the heat from the sun is fully nullified. Despite the great atmospheric pressure and the lack of light and heat, life still thrives in these environments. One of the factors that facilitate life at these extremes are the geothermal processes (vents in the sea floor) which are purely disconnected from the events of the sun, and completely powered by our magma core.
As we know, many planets are suspected to have molten cores, which are the result of their formation and which will continue to remain such for billions of years (we will probably be wiped out by our Sol turning into a red giant before our the Earth's core will lose it's energy). As such, though it'd be near-impossible for life to survive on the surface of a planet that is not a part of any solar system, under the surface life could be bountiful.
1. http://books.google.com/books?id=o6OmdAFDTVQC&lpg=PA233&...
That's page 244, and from there until the end of the chapter (p.250) is all relevant to your comment.