Asteroid thermal power

So. They talk about creating big satellites with tons of photovoltaic cells on them to create power from the sun and beam it to earth on microwaves. The reasoning, I believe, is that there is no atmosphere to attenuate the light, and it can be put in an orbit that leaves it in the sun at all times. (Although at the same time you might want it in a geosynchronous orbit, if you were constantly beaming down energy, and I don't think you can do both of those at the same time. (But whatever. It can just fill up big wicker baskets with energy and parachute them to earth, to be picked up by anyone.)) Regardless, my idea is that we just drag free floating, small asteroids into that same orbit and get them spinning so that one side is always facing the sun (with thrusters to keep them that way). One side of the asteroid would be very hot, and the other would be very cold, as they always tell us about the sides of the moon or whatever in astronaut books. Then fit them with heat transfer type energy production devices, like in geothermal plants, heating up water on one side of the asteroid and transferring it to the other to be cooled and go through turbines or whatever. (Oh wait. On earth the movement of water uses gravity and density differences doesn't it? Well. I am sure there are just dandy alternative ways of using the hot to cold difference to generate energy.) I dunno how expensive each option would be, but that is the not-baked part. Maybe this method would be more efficient than building solar panels and satellites and sending them up. And maybe with the kind of asteroid friendliness we would need in order to pull them near earth, we would be in a position to just mine whatever materials we needed to build the plants out of other asteroids anyway. And if you want geosynchronous orbit, just build a bunch so there are always some in the light. Who needs power at night anyway? :-)