Here's a theoretical paper that asks an interesting question: When the solar system was very young and still very hot, could medium-sized asteroids have been habitable abodes for life? It's not a crazy question, because there's abundant mineralogical evidence for what we consider the building blocks of life in asteroids, specifically carbonaceous asteroids. They contain lots of different organic molecules including amino acids; there's evidence for the presence of liquid water within asteroids in the past, and many carbonaceous asteroids still retain quite a lot of water bound within their minerals; and the residual heat from their formation and from the decay of radioactive isotopes give you the "food," water, and energy that are necessary for life. But despite searches there's been no convincing evidence that life ever arose on an asteroid. Given what we think are the right ingredients, why didn't life arise?
Oleg Abramov and Stephen Mojzsis developed some computer models to try to figure out an answer to this question, exploring theoretical asteroids with diameters of 75 to 200 kilometers beginning at about 3 million years after the initiation of solar system formation. These asteroids retain initial heat from their formation, and then experience further heating due to the rapid decay of aluminum-26.
The paper tells an interesting story for what happened within young asteroids, which would have started out containing some rock (part of it in the form of the common minerals olivine and pyroxene), and some water ice, and some pore space. The asteroids' interiors heat rapidly at first and then more slowly as the aluminum-26 decays. At an age of about a million years, the inside of the asteroid gets warm enough -- above 273 Kelvins -- for the water ice to start melting. This part of the story is independent of the starting diameter of the asteroid.
Once the water starts to melt, the story gets more interesting. If there are minerals available that like to react chemically with water, those reactions get started. The common minerals olivine and pyroxene do react with water, very readily in fact, turning into a mineral called serpentine. This is an exothermic reaction, meaning that heat is released as the reaction proceeds, warming the asteroid a bit more, which melts more water, which reacts with more olivine and pyroxene, and so on; it's a positive feedback cycle.
The final outcome depends upon how much water Abramov and Mojzsis gave the starting asteroid. If it was 20% water, all of that water gets used up to make serpentine (or, to put it another way, water is the limiting reagent in the reaction), and the final asteroid winds up being dry and hot. With more than 20% water, there is water left over after the reactions have run their course, and because of water's capacity to absorb heat, the resulting asteroid is cooler.
What happens next depends upon the initial size of the asteroid. Larger asteroids take longer to heat, they get hotter, and they take longer to cool. This shouldn't be any surprise to anybody. With more initial water content, the maximum temperature inside the asteroid is cooler and is reached later. They found heat to be retained longest in a 200-kilometer asteroid that started out as 40% ice, a body that took 60 million years to cool. This body would have contained habitable conditions at its center (liquid water at temperatures between 273 and 373 Kelvins) for over 24 million years. Is this long enough for life to start? It would seem like enough time, right? So why didn't it happen, as far as we can tell?
Abramov and Mojzsis looked more closely at what happened within the interior of this asteroid over that 24 million years and may have found the reason why life couldn't get started. When an asteroid's interior gets hot enough to melt water and that runaway serpentine reaction gets going, the center of the asteroid actually gets too hot; the Goldilocks zone is fairly close to the surface. As the asteroid cools off, the habitable zone migrates inward: regions closer to the center become cool enough as regions closer to the surface become too cold, freezing the ice. The cooling happens pretty fast, so the habitable zone migrates inward at rates of around 1 to 10 millimeters per year. (It happens more slowly for larger asteroids with more initial water.)
This is an important number, because recent research has shown that although asteroids can be very porous, the pores are tiny (5 to 50 nanometers across) and not well-connected, so liquid water cannot migrate from pore to pore very fast, if at all. Water, and any nascent life floating in it, certainly couldn't have moved fast enough to keep up with the migration of the habitable zone. The smallest known non-virus life form from Earth is 400 nanometers across, much bigger than these pores. Even at the centers of the largest asteroids, where water would have hung around the longest, pre-biotic organic chemicals wouldn't move around readily. So opportunities for reactions between naturally occurring organic molecules would be very rare.
Big asteroids are a different story. Big, ice-rich bodies like Ceres, or the body whose destruction gave rise to the Themis family of asteroids, would have differentiated, separating into layers of liquid water above a rocky interior, solving the pore space problem. Their long-lasting internal heat would likely have kept those oceans liquid for millions or tens of millions of years; Ceres may even have retained an internal ocean right down to the present day. So the moral of the story is: despite the existence of habitable zones within medium-sized asteroids for many millions of years, it just doesn't seem like life had a chance to get started there. But we ought to check for ancient life on Ceres and Themis!