<i>By shielding, do you mean that astronauts could live inside or behind the asteroid, just using its mass between them and the sun?</i><p>I mean that the habitable modules would be located inside silos embedded within the asteroid, so that the living space would be entirely surrounded by radiation shielding mass.<p><i>That would be pretty dark and cold.</i><p>The problem in space is generally getting rid of heat. Vacuum is a great insulator, insulation material is effective and relatively cheap, and radiative cooling is fairly slow. The other thermal problem is exposure to direct sunlight. The asteroid as a shell of massive shielding would help in this regard.