There are a couple problems. Basically, the first is that whatever is generating the power needed to move that heat off-ship is itself a huge heat source, and if there are any inefficiencies at all in the power generation or thermal transfer systems, there will be additional waste heat that needs to be moved and dumped. If you thought hiding a room-temperature human crew was bad, the thought of hiding a fusion reactor should probably make you wince. Most radiators have efficiency issues when radiating into a limited cone; some form of laser or other forced directional emissive cooling system to dump the heat also has the issue of generating heat which also needs to be dumped. Basically, you quickly start chasing your own tail; dumping heat requires generating heat, which needs to be dumped as well, which generates even more heat...
The second is that you need to know where the enemy is in order to send the thermal energy where it is not; it becomes rather trivial to detect thermal radiation methods of heat exchange by using fairly minor probes, but this does necessarily presuppose a competent enemy (that is, if you can solve the other problems, you might be able to sneak up on someone who isn't looking for you).
There are other issues, but not all of them are related to Aurora. For instance, Aurora's propulsion system means you don't need to use detectable burns to maneuver. Instead, you just turn off the TN drive you're using and you instantly stop, based on inference from what happens when you take engine damage. That, unfortunately, also does mean that the power problem above gets even worse, because you need to keep the TN drive continuously active (with all the power demands and thermal issues that entails) just to keep moving. Moving on conventional reaction thrusters would fall into the "detectable burn" problem, where any maneuvering you do will stand out like a floodlamp at midnight. That said, you can drive TN drive emissions down ridiculously low as mentioned above in Aurora, so we can probably just assume that was solved at some point.
Basically, stealth in space, to me, is not in the art of making yourself unseen; that falls prey to thermodynamics. It's in deception and misdirection; making the enemy believe that what they've detected is something other than what it actually is. If they think you're a freighter, or another NPR, or even an asteroid or other natural astronomical body (even though asteroids don't have non-circular orbits in Aurora - or, I suppose, even orbits if you turn off that option), that may alter their reactions. That, obviously, isn't modeled in-game, however, though it'd be fun if it were someday. Can you imagine stealing someone's IFF and using to launch an alpha-strike on another power? ^_^