Bah, I jacked another thread.
Linguofreak, it doesn't violate thermodynamics, otherwise a radiator wouldn't work. The universe gets a little hotter from the laser (which increased total entropy).
Actually, the universe gets a little cooler from the laser. An object is not "hot" unless it has both energy and entropy. A laser beam is basically an object in which all the particles (photons, in this case) are moving in the same direction at the same speed. In the same way, an ice cube cooled to absolute zero and accelerated to an arbitrarily high speed will have all of its water molecules moving at the same speed in the same direction. It will still be very cold, no matter how fast it's moving. (Note that this doesn't say that things won't heat up when the ice cube/laser hits something. But that has nothing to do with the entropy changes involved in the creation of the laser/ice cube).
Basically what you're trying to do is like trying to keep your refrigerator cool by using the temperature gradient between the inside and outside of the refrigerator to operate a device that sucks in air from inside the refrigerator, cools it off, and pumps it out of the refrigerator. The first problem is that you would be better off trying to pump the cool air back into the inside of the fridge. The second is that the only way you can get energy from the temperature of your environment (or more accurately, from the temperature differential between your refrigerator and its environment), is by letting the temperature of the refrigerator get closer to the temperature of the environment.
Basically, a radiator gives off "hot light," the light goes off in whatever random direction it chooses, and thus has very high entropy. A laser gives off "cold light" with very little entropy, even if it has alot of energy.
So if the ship is hotter than its environment, a laser might work for cooling the ship off, but a radiator will work better. It doesn't try to cool off the energy it emits before it emits it, so you dump more heat overboard for a given amount of energy dumped.
If the ship is colder than its environment, you simply cannot use a laser to keep it cool. You may be able to use a radiator, *if* you have some other source of energy than the temperature differential between inside and out (This is basically how an air conditioner or fridge works, but both require a source of power, you can't just run them off the temperature difference between inside and out).