Pebbles in the sky
Obviously, the reference is to Asimov's masterwork. But, why pebbles? Because in this chapter we are not talking about true planets, but about moons. More precisely, about Jovian and Saturnian moons.
I talked you about the possibility of stellifying gas giants. The most important thing about this is that the new stars would have their own stellar systems. Among the hundreds of natural satellites, five are planet-sized: Io, Europa, Ganymede and Callisto, which orbit Jupiter, and Titan - Saturn's largest companion. You may see them "dissected" in the picture above (in that order). Yes, I know, these pictures are quite small, but you may see such images, with their legends and explanations on the Internet, for example on Wikipedia.
Now, let's see what is the main problem with those bodies, and then I'll come back and describe their structure. The main problem, as you already guessed, is that they are too far away from the Sun, they are cold and dark. That's why few people thought of terraforming them (the only paper I've read on this is Zubrin's "Entering Space", envisioning HUGE orbital mirrors to be used for this job). But, let's suppose that we do the trick with turning the giant planet into stars. What would happen then?
Well, it's hard to estimate, since nobody tried before, but the first logical consequence would be a luminosity increase. For proper ("main sequence") stars, there is a proportionality between luminosity and the 3-4th power of its mass. At the ends of the interval (very large or very small stars), things change. Brown dwarfs can be 25,000-100,000 times fainter than our Sun (depending on their mass and age), although they only fuse deuterium. Jupiter is currently around 90 billion times fainter than the Sun. But, by triggering proton fusion, it could be at least as bright as a brown dwarf. It seems too little, isn't it? No, because the irradiance received by a planet from a star also depends on the squared distance between them. Callisto is about 100 times closer to Jupiter than Earth to the Sun, and the other moons are even closer, so just do the calculations. Stellification might just be the key to terraforming those moons.
Another problem would be the radiation belts. Ganymede, Callisto and Titan are rather safe, but, for now, Io and Europa lay inside Jupiter's radiation belt, which would be a problem for humans. But remember that each giant should lose at least one tenth of its mass during the ignition. For Europa, at least, that should help getting it out of the dangerous zone. Also, the extreme volcanism on Io would be slowed down a bit by Jupiter shrinking.
Now, let's see these moons' structure. First, they all have a Moon-like surface gravity, which isn't very good for building and holding an atmosphere, but not very bad either (see Titan). Io is the only rocky one, with a metal core and a rocky mantle and surface. All the others have metal and rock cores and the outer layers made mostly of lighter elements, mostly water. It seems that there is an icy "lithosphere" (a few kilometers thick on Europa, much thicker on Callisto), followed by a layer of either liquid water, either exotic kinds of amorphous ice.
Probably, the icy crust also contains carbon dioxide, ammonia and other stuff needed for an atmosphere, (Titan already has a nitrogen atmosphere, with some hydrocarbons) so letting it melt under the new star's light should be enough (if it isn't we should import some, maybe even from the smaller satellites in those systems). Let's hope that minerals are also present in the lithospheres and mantles of the moons, otherwise we would have a problem. Some are very enthusiastic about this and would want to melt down all the ice, in order to get to the "ocean" (as media usually calls it) beneath. Be aware, it's not an ocean, it's the mantle (more likely, it isn't liquid water at all), and melting all that we see would turn each of these worlds in something like Kevin Costner's "Waterworld" (or the post-apocalyptic world in the "El Barco" series, if you prefer). People need continents to live on, that is massive rocky structures. Diverting rocky asteroids to the moons would be quite a daunting task for now, so you may put this on the "cons" list. Once more, making a plan for terraforming these bodies is difficult due to our little knowledge about their structure.
Once we create atmospheres, melt the ice and hopefully leave some unflooded landmasses, we could begin proper terraforming. The process is the same as for Mars, so I won't bother you again with all the succession.
The big "pro" of trying to terraform these big moons is that this would bring us another four or five habitable worlds.