There are a few fundamental problems with laser cooling in space in the first place. For one thing, there's really noplace for that heat to go. Vacuum is a rather good insulator, so if something gets hot, it will take quite a while to cool down. Unless one uses some exotic method to bleed off the heat, like in bursts of steam or something (wouldn't that be an interesting sight?), it doesn't "just go away". Any cooler has to work pretty much by moving heat away from the laser and into the structure of the ship.
Which brings me to my .02 CR for this post. Ships should not all cool equally well as they do in the current game. Bigger ships have more mass for heat to go into the structure. I would think that the lasers would cool slower each time they're heated up in a given battle. For the first few bursts the difference would be negligible, but in a longer fight the laser temp cool-off would eventually drop to a near crawl since whatever sort of heat exchanger is moving heat from the weapons to the structure of the ship will be taxed more heavily and the structure will already be somewhat heated up, so there is less of a temp differential for the system to work with.
On smaller ships, the effect would be noticed quicker, since they have less mass/structure to dump that heat into in the first place. They're maybe more nimble or accelerate faster, since they are small, but I think their lasers should heat up a bit quicker and cool slower. It's the tradeoff for being a smaller target with good acceleration and turn.
Bigger ships, especially actual warship,s might have more of a ship to dump heat into and possibly special gear to dump heat faster, but still it's not an infinite capacity as it is now.
Other than not being able to fire the laser, overheating should have other consequences. As heat is dumped into the structure of the ship, cabin temps would rise. At some point, other equipment would also start to fail as ambient temps go up and the efficiency of things like processors and memory storage are hampered or possibly they heat up to the point of a fail and simply blow out. It might ruin some delicate types of cargo as well, in extreme cases.
Yeah, I know, "don't let reality interfere with gameplay". But consequences of heat could be used to increase the pressure on the player in longer battles that more advanced players might get into, making the player have to fight smarter and be more careful to make sure laser shots pay off enough to take them. For a beginning player in the typically short fights against one or two opponents, the difference would be negligible. It would be something one gradually learns to take into account as one gets involved in bigger/longer fights.
As far as different colours of lasers.. Different colours of laser can affect different hull materials to a greater or lesser extent. Consider for a moment common laser "pointers" of our time. If you get hit in the eye by a red laser pointer, chance of damage is less than for a green laser of the same power. Why? Your retina is full of capillaries that are full of blood. Blood is red, which can be more accurately stated as "it reflects mostly red light". If it is hit with green laser, it absorbs more of it and heats up more. More damage.
If hulls are made of different materials, or adding something like IronHide changes properties of the hull, then different colour lasers might be a bit more or less effective against different materials. And even if the difference is actually negligible, you won't be able to tell a combateer that! They'll have their personal beliefs, and marketing will be taking advantage of that by making desired colours available, at least at a price.
