With regards to your cooling problem, what propulsion system is common for the warships in your scifi universe? If it's something with a fairly high mass flow rate you can dump waste heat into the propellant and eject it out the back (nuclear thermal rockets are self-cooling for this reason). Another solution is to store the waste heat in a reservoir of some kind. Now, of course one possibility is the propellant, like I mentioned above (the pressure in the tanks will then increase until it becomes a good idea to get rid of it - through the engines), but you can also use a big block of metal, or some part of the ship's structure if it is big and beefy. These are "peak usage" solutions for when the spacecraft is firing energy weapons or making more waste heat than it normally does (or has retracted its radiators for combat). At some point you still have to eliminated this heat by radiation, which is the main problem you're trying to deal with. Does your spacecraft produce so much waste heat on "idle" or have non self-cooling engines that make a bunch of heat, that it can't make do with (relatively) small or retractable radiator surfaces? How about a liquid-droplet radiator?Starships in my world are big. Really big. They have to be; because hyperspace is tachyonic in nature, mass is speed. The conservation laws don't work quite right in hyperspace.
Spacecraft design is my hobby, and I have a physics degree to back up all the engineering reading I've done on the topic, so this post was naturally of interest to me. If you shoot me the specs you're trying to work with (propulsion type, size, mass, powerplant type, expected performance) I'll see what I can do in terms of making it work with realistic (if futuristically powerful and efficient) equipment. If nothing else, I'll be able to give you a ballpark estimate on how much heat your handwavium hyperspace cooling system needs to eliminate.
Actually, most of the laws of physics don't work right in hyperspace. Matter and energy don't exist there as we understand them; what exists instead is a mishmash of entangled states, and in fact if you wish to remain alive and in one piece while traveling in hyperspace, your ship must be protected by a field which normalizes the laws of physics.
But I digress; the point is, ships are typically several kilometers in length and mass hundreds of thousands (if not millions) of tons. Anything smaller will either be too slow or simply disintegrate.
This mass is useful, though. It takes months to travel between stars. There's a "time-distance" curve; the farther you travel, the less time it takes per light year. A trip from Earth to Gliese 691, about 30 light years, might take three months; a trip from Earth to Regulus--which is roughly 2.7 times as far away--would take perhaps five. And because trips take so much time, there must be hydroponics, cold storage, and other food supplies; water must be recycled, air replenished, etcetera. Some ships carry their own fuel refineries, in order to separate deuterium from water, methane, ammonia, etc.
Which brings us to the propulsion: in normal space, ships are propelled with fusion thrust. Open fusion bottles with superconducting magnetic nozzles--and for better efficiency, reaction mass (depleted feedstocks: water etc) is injected into the exhaust. Shipboard power is also supplied by fusion.
I have trouble with the "dump waste heat overboard in the exhaust" model because I don't see how it can work, thermodynamically. When you pump heat into a heat reservoir, you're running a refrigerator--pushing energy uphill takes more energy and generates, rather than eliminates, waste heat.
And I really don't want to have to rely on venting coolant overboard; that will only make trouble. (In any case, when the ship is in hyperspace, the main engines are off-line because you can't change your speed or direction once there; besides all the other wierdness, it's also a timelike space.)
The weaponry on the other hand, is generally self-cooling. I prefer catalytic lasers for energy weapons, for a variety of reasons, and the expended catalysts suffice to carry away most of the waste heat. Beam cannons run in the 10-20 megawatt range for lightly-armed ships, but most ships have at least basic armaments because it's a dangerous universe out there. Otherwise, ships also use nuclear-tipped missiles of various yields.
Passenger ships in the period I write about typically have a maximum acceleration of about 50 g, and are inertially damped to keep from turning the occupants to jelly. Military ships can do better, depending on design. Inertial damping, of course, causes its own energy problems, with the conversion of energy between types and all.
I have seen real hard SF writers get away without discussing these kinds of issues, and it's probably only my nigh-anal-retentive attention to detail that makes me want to have a plausible way of dealing with the engineering concerns. None of this is really critical for any story I want to tell, after all.
But it is fun to think about.