Andrew: Thermodynamics says that any attempt at "directed heat discharge" is going to produce more (undirected) waste heat. The second law can get really annoying at times. 
Holding shrouds in place faces the problem that the shrouds themselves will heat up and produce a thermal signature - though, true, perhaps a more diffuse one if they're really big. (More diffuse, but then also larger in area - somewhat of a wash.)
Not quite. The second law is a global statement: the entropy
of the universe is monotonically increasing. You can cheat locally by consuming "free energy" (which is a technical term in thermodynamics - it basically means "energy which is available to do work without violating the 2nd law"). This is what an air conditioner does - it makes the coolant colder and the radiator fins warmer at the cost of burning fuel/consuming electricity which results in the warm radiator fins needing to also absorb the waste heat from the burning/consuming and therefor becoming even warmer.
The way this applies to a "directed heat discharge" is to imagine having a spaceship with a really good refrigerator, a really good battery to run it, and a refrigerated spherical shell with a hole punched in it (to radiate the heat). You probably also want the interior of the shell to have a high reflectance/low absorbance so that not much interior heat leaks into it (you could also insulate it really really well) which cuts down on the work the refrigerator has to do. You use the refrigerator to keep the shell cooled to 3 degrees kelvin (background temp). This makes the ship (inside the shell) heat up more and more - as it heats up, it glows and will radiate thermal energy. Most of this energy will be reflected by the walls of the shell, except where you've punched the hole in it, where it escapes to space. The problem with this technique is that you lose radiation efficiency as you make the hole smaller/more directed. One way to to get around this would be to stick a (refrigerated) parabolic "mirror" outside the shell, with a radiator at the focal point of the mirror, and with the mirror having high reflectivity in the vicinity of the peak of the black body spectrum for the radiators operating temperature. This would allow you to get (almost) 4pi solid angle of radiation from your radiator, while directing the radiation into a "beam" that the bad guys would need to be lucky to intercept.
The upshot of this is that, as long as you have a free energy source (i.e. fuel) you can selectively refrigerate parts of your ship so that they don't show up like a spotlight on the bad guys' thermal sensors, unless the bad guys happen to be looking "up your kilt". This does not violate the 2nd law in the same way that the refrigerator in your kitchen doesn't.
John
