Mentioning heat reminds me of another lulz: stealth in space.
The most trivial issue being stealth while having the thrusters on, like both the Romulans and Klingons do all the time. I don't care how you bend light around the hull, you're ejecting a huge trail of very very fast particles. Whatever particles your engine produces. A lot of them are going to be ionized (or even all), and they're going to be fast, which means they're going to just emit a lot of high energy photons. (Which in turn ensures more willl be ionized.) They'll interact with the matter around in space, for even more photons, and they'll scatter light from the local star like a comet tail.
Briefly: even if your ship itself is 100% invisible, that won't do you much good when you have an AU worth of glowing trail pointing at you. It's like trying to make a transparent bullet... which is also a tracer. No matter how good you get at the former, the latter will mean it's still very visible.
But let's say you just coast with the engines off for most of the approach.
Well, here comes problem #2. The cosmic microwave background has a temperature of about 2.7K. Unless you're at that temperature, i.e., about 10 degrees lower than when hydrogen starts solidifying on your hull, you're going to stand out in the infrared or microwave spectrum.
And in practice you're going to be a lot hotter than that, because you have to SOMEHOW dissipate energy. Every human, every computer, every piece of machinery running, every lightbulb, is going to produce heat. And your ONLY way of getting rid of it is to go Stefan-Boltzmann on its ass, and basically have some radiators that release it into space. Like the panels on the space station. Most likely it's going to be your hull, since it's already big and pointing outwards.
And it gets worse if you look at stuff like the insanely high power output of warp cores in ST, and the about 17.8% efficiency we calculated. They're going to release about 5 times their rated power output as heat. Which you have to release in space somehow. Those spaceships are going to shine and stand out like a star over Bethlehem.
Fine, someone will say, we'll just have the radiators pointing backwards, so whatever we're attacking doesn't see the infrared. Not so fast. First of all, SOME heat is still going to leak through or along the hull's metal. So you're just standing out a little less, but you're still standing out.
Second, that still only helps within a cone to the front of the ship. Now you made it MORE visible from behind, since all energy is going out that-a-way. Any half-way competent enemy will figure out how to counter it, at least within its systems: have a number of detection stations or drones scattered all around the system, and scanning in all directions. It doesn't even take many to make it impossible to hide your heatsinks from ALL of them.
And even in deep space battles, anyone who's encountered your stealth ships before, will be accutely aware that you're only hidden from one direction. So what can they do about it? Well, just launch half a dozen torpedo-sized drones that scan for infrared in a full 360 degrees.
They can be very small and cheap, in fact, so even a small vessel like the NX-01 could carry hundreds of them. And unless you shoot them down, they're reusable. And if you DO shoot at them, well, you just signalled where you are.
