I don't see how it breaks the laws of thermodynamics. It really works exactly the same as any other radiator it's just that the coolant moves freely through space instead of within some pipes.
So, is that a good idea? Well we get to get rid of the mass of those pipes, but they were doing something (containing the coolant). How hard is the collection problem? It's certainly not impossible.
With respect to conservation of momentum: if the collector is connected to the main ship (with a tether or otherwise) the situation is identical to if the coolant was flowing through pipes. If it's not? Remember that as the coolant is ejected it gives an impulse to the ship in the opposite direction. The collector collects it and recieves an opposite impulse. If it's not connected to the ship it will need to fire rockets to catch up to the ship, but the net effect will be the same as if the main ship had fired it's rockets in the same way, so just set it up to go in the direction you want to travel in. If you don't want to change course or speed then a tether is a better idea, but we're talking about a very small impulse here and course corrections are probably going to be required pretty frequently so I don't see this being an issue.
Anyway, I'm not saying it's a good solution to the problem of radiating heat in general. I'm saying it could be a good solution to the problem of radiators being an attractive target. Go for a more complicated and less efficient system of radiating heat in order to make a smaller target.
You're answering that to my objection that you'd need a collector that's a 12 km sail floating behind your ship, you know? How in Lucifer Morningstar's good name is that making your vessel SMALLER? Now instead of having a, what, tens to hundreds of meters worth of radiators as a target, I have something the size of a CITY that I can shoot to disable you. Because if your collector is in pieces, you're not going far before you overheat
Hell, I don't even have to completely shatter it. Disable some thrusters on it, and it'll never catch up with you.
You want a smaller vessel, here's a simpler idea: according to Messrs Josef Stefan und Ludwig Boltzmann, the heat you radiate is proportional to the 4'th power of the temperature of your radiator. So you just put a heat pump between your craft and the radiator. Hell, deck the radiator in Peltier plates.
So, say, you want to keep the interior of your galactic battleship at a comfy 25C or so. You know, light uniform kinda climate. You could just circulate your coolant directly, and have your radiators also at 25C (actually, lower, because they've already dissipated some, but let's ignore that for now). Or you could make it a big refrigerator, and have the radiators go up to, say, 325C. The difference is 300K vs 600k when radiating heat, so a 16 TIMES factor per surface unit.
There we go. Now you can make your radiators 16 times smaller.