Choice of coolant
As others answers mentioned, the best coolant is water, at the range of temperatures you can expect for your laser. It absorbs heat fast (great thermal conductivity), absorbs a lot of it to raise 1 kg by 1 K (great specific heat), and absorbs even more when melting (great latent heat of fusion) and when evaporating (great latent heat of evaporation). Note that you would store it frozen to get the full benefit of it.
It also makes for a rather good propellant for nuclear-thermal or nuclear-electric drives, so your ship is probably carrying those as propellant, not lugging otherwise-useless tanks of heat sink.
If your tech needs cryogenic temperatures, liquid hydrogen is by far the superior option. It has the best specific heat ever, and a pretty good latent heat of evaporation.
There is in fact a hypothetical type of spaceship that achieves partial stealth by being a giant tank of liquid or frozen hydrogen and a Vantablack coating, the hull being cooled down by evaporating hydrogen to an extremely hard to detect 14 K. (See details on Atomic Rockets) Whether or not the stealth aspect itself would work is up to debate, but the ship itself, if big enough, could stay out there in the sunlight for years at a time - hydrogen is that good.
On the other hand, hydrogen is absurdly low-density, and armoured warships may want not to have giant fuel tanks. Either they would be exposed to enemy fire or they would require vast quantities of armour. And armour is heavy, which is bad for a spaceship. As you probably read many times on Atomic Rockets, every gram counts.
Similarly to water, those hydrogen tanks are probably your propellant in the first place. Hydrogen is the most efficient thermal propellant by mass, after all.
If you need to deal with very high temperatures and don't want to use water - which can be corrosive or even dissociate in hydrogen and oxygen - you may want to go for sodium.
Its specific heat isn't that great compared to the others, but its boiling point is much higher. It is in fact used as coolant liquid in some nuclear reactors.
So while it wouldn't be your propellant, those sodium tanks would instead be your coolant reserve. Again, you would have it anyway, and sacrificial heat sink would be an emergency secondary use.
In a spacecraft, anything bigger than a short-range capsule has radiators. The ISS has them (those big accordion panels at an angle with the solar panels), the Space Shuttle had them (lining the inside of the cargo bay doors)...
Future spaceships, especially warships, will have enormous power sources (be it powerplants or even often the drives themselves) that will need enormous radiators to get rid of the waste heat.
Note that varied components will have varied ideal temperatures, for example crew quarters at 300 K and nuclear powerplant at 1400 K. While you may be tempted to use heat pumps to equalise temperature, it adds complexity and is impractical for large temperature differentials, where they become massively inefficient.
Instead, each component with a different temperature will have its own sets of radiators. Probably small ones (like on the ISS) for crew quarters and bigger ones, possibly glowing red, for the powerplant. Some for your cryogenic components (like those water tanks as well) Maybe some more for varied weapons as well.
In general, when designing a component, you want it to have a working temperature as high as possible. That's because the radiator efficiency goes up with the fourth power of the temperature. And you want your radiators to be as small as possible, because not only are they heavy but they also make for great targets.
The upside is that radiators are visually awesome and make your warship look badass. Nothing conveys (quite literally) a sense of power like two giant orange-glowing sails.
Venting heat sinks
So your star cruiser has retracted its radiators to avoid getting them shot. Or some of them have been ripped off by enemy fire. Or its weapons generate so much waste heat that even its full radiator complement can't get rid of it all in combat conditions. Heat sinks are filling up...
Why vent them?
Ideally, you want to keep them around as long as possible. After all, once combat is finished, or even if orbital mechanics temporarily put you out of range, you can then use your (remaining) radiators to cool it back down.
The problem starts when it vaporise. Which is almost immediately with liquid hydrogen. With water, you have some more time, and sodium, as noted above, would only go so hot in case of emergency.
Now, you could keep it under pressure to prevent it from vaporising in the first place, which is probably only practical with sodium. It is easier to harden a coolant system than giant propellant tanks, hot hydrogen tends to escape through walls and hot, supercritical water is one of the most corrosive substances there is.
But if you prevent it from vaporising, you can't make use of its latent heat of vaporisation. In case of emergency, you may simply not have the choice.
So it start vaporising, then. Its volume increases massively - for example, water vapour takes about 1250 times more volume than liquid water. You simply don't have the volume to keep it on board.
You could use it to fill a balloon, but that means you are lugging around a rather massive balloon around just in case (which is very bad - again, every gram counts), and that thin, unprotected balloon will make for a nice big target for the enemy.
So when things get that hot, keeping it on the ship is simply not an option.
Venting it - water or hydrogen
With water and hydrogen, in fact, that's already part of the design. Remember, those are your propellant first and your heat sink second. So to vent it, you send it to your thrusters.
The thermal drives you are probably using right now works by heating up the propellant as much as possible and then letting it expand as much as it wants through the nozzle. Today's chemical rocket drives are a special case where the heat is produced by a chemical reaction between the propellants, and the byproduct of the reaction escapes through the nozzle. Your futuristic drive is probably heating inert propellant through a nuclear reaction (nuclear-thermal) or with electrical power, itself from a nuclear powerplant (nuclear-electric).
In fact, this is already used today, with regenerative cooling: rocket nozzles get so hot that to stop them from melting, still-cold propellant is sent flowing in its walls before going to the reaction chamber.
Here, it's the same thing, except that the propellant is flowing through your coolant system and/or varied component first.
So what it looks like? Your engines are used. If you can't afford to use the engines in the first place (maybe because it would add more heat than you can spare), then it will look like cooler water vapour/hydrogen is flowing from it, which will generate less thrust. You may or may not see some white in the plume as expanding (and thus cooling) water vapour condenses into crystals in that case.
Note that in space, even when working at full thrust, those drives are rather hard to see. The plume may be entirely invisible, and you would see it working only by the ship moving and innermost parts of the nozzle being heated white.
Venting it - sodium
If you can, try and vent sodium vapour through your nozzles as they are firing. This will give you a little bit of extra thrust as the heavier atoms are used as propellant, which is always good to have. This may colour your plume orange, I suspect. If so, this would make for great visuals, as orange plumes show how desperate the fighting warship has become - either because they overheat or because they need every little bit of extra thrust.
But this may not be an option. After all, sodium may condense against the nozzle interior or some component of the chamber, and mess everything up. They may clog something, interfere with nozzle cooling or even fracture it with heat differences. Or your drive may simply not allow it, for example if you use Orion-style external nuclear pulse propulsion (aka pushing a plate with nukes) or other nuclear-detonation-based systems.
So your warship's coolant circuits may have escape valves. Those will probably look like tiny thrusters, and have doors to close them when not in use. When heat or pressure in the circuit is too high, they open and let sodium vapour escape.
They are, essentially, thermal drives, just like your main drives but using sodium instead. Sodium being heavy, it gives good thrust but bad efficiency, and can be seen as such as far as movement goes. They will be shaped like your main drives, for thrust efficiency, but that's because you want the plume to diverge as little as possible (which is the same here). After all, you don't want the plume to hit your ship's hull and condensed sodium and coat everything.
For the same reason, they may optionally extend when in use, so the venting point is as far from the hull as possible - but remember, it will have to be a rigid bar instead of a simple hosepipe, or the thrust will send it flying against the hull.
Given the temperatures, it will probably glow orange at exit point, turning red just a bit further in the plume (at those temperatures, it cools down fast), then as a thin cloud of condensed sodium droplets. Given the energy, it will disperse fast, and disappear pretty much instantly as soon as it stops venting.
Venting itself will probably be done in short bursts, to use only as little as necessary, and to avoid exposing a firing valve as much as possible.
Addendum: why thermal drives?
Thermal drives are much more efficient than chemical drives (though they generally give less thrust), but their mileage is rather awful compared to electric drives like, say, ion engines. So why would the star cruiser use thermal drives instead of those?
That's because for a given energy, you can either have great thrust (chemical drives), great efficiency (electric drives) or a balance (thermal drives). And you can use only so much energy in a drive before it vaporises.
So those electric drives have awful thrust. Which is OK for an interplanetary probe, but your star cruiser will probably need to manoeuvre, for example to avoid incoming enemy projectiles or avoid spending months or even years getting out of deep gravity wells.
The star cruiser may also have a set of electric drives with milligee thrust for slow, interplanetary manoeuvres, when it has time for long-duration thrusts and no giant lasers to eat half the powerplant's output, but it will probably run on thermal drives when fighting.