That doesn't actually work, you know. It's science fiction for a reason*. In reality, the rock would have disintegrated pretty quickly. Also, you don't seem to have your scales right. A small asteroid is a few kilometers large, a large one has a diameter of 300 km or more.
1) Keeping the asteroid in a semi molten state is problematic. Liquids vaporize pretty much instantly in a vacuum, after all. Also, asteroids are large, and most of the larger ones can be up to 50% empty space by mass.
2) The hole through which they inserted the comet is a weak point, and would result in the bubble bursting as soon as the expansion started. Additionally, the sudden cooling would crack up the hull, and introduce numerous failures amongst the hull. The chances of getting a balloon like expansion are very, very slim.
3) You're not likely to find an asteroid containing 7 trillion tons of Iron in a reasonable timeframe. That's a lot of Iron, you know. Iron is a rarity in asteroids, after all. The majority of the asteroids are simply bunch of debris, rock and ice, with up to 50% empty space inside. I don't think there are any that apply. ((Unless I miscalculated, which is a possibility, you require a 10*10*10km cube of iron to make that work.))
Additionally, ramming in space is never a good idea. Even a small object has tons of kinetic energy, and the shell might protect you from a while, but a properly steered and small enough object will penetrate.
*If the series is the one I think it is, I doubt you should trust the science. It has things that might just work, but with any technical troubles waved away in spite of a message.
Here's a list of asteroids