It is not the heat but the ultraviolet that would kill the trolls.
I don't think it's either. Apparently moonlight can hinder trolls as well as sunlight. Now the moon only reflects the light the sun gives off, and mostly in the visual spectrum. Little or no UV gets reflected, and the little that did would be defused by the atmosphere. It also doesn't give off heat. So, I think it's the actual light from the sun or moon. This may be a magical thing, since both are seen as deities in most cultures. Does man-made light stop trolls is the question.
That's an interesting thought. I hadn't really thought about why the moon discourages trolls as well as the sunlight. It could be that ultraviolet does kill trolls, which leads them to be conditioned to avoiding light. While the moonlight wouldn't kill them, it could still be a deterrent. If that's the case, then man-made light should work as a deterrent as well, since they're just avoiding light in general. They might be able to differentiate between natural and unnatural light, though, so I can't really say for sure.
On the other hand, if it's some kind of magical property of the sun and moon, then we don't know that they have a conditioned (or instinctual) avoidance of light in general. Man-made light may work, but it also might not. What's interesting to me, though, is that trolls are able to survive in moonlight. On the train ride, the threat level was lowered, but only to a 7/10. That implies that the moon would either be a lot weaker than the sun, or that it's not diametrically opposed to trolls.
As for UV killing trolls...they would survive that just as easily in a hot climate as they would anywhere else in the world. That seems kinda irrelevant to me.
If you're an aircraft carrier and you had personnel transfer in the 48 hours between day 0 and day 3? All dead. Floating tomb.
Remote, sparsely inhabited island with a bed and breakfast for tourists? All dead. Or trolls.
So from the point of view of imagining intact societies, we're faced with an interesting situation. In some ways it simplifies things. It doesn't really matter so much who has what equipment or training, or which kinds of geographies help or hinder human survival. It all really boils down to one thing: were you cut off from the rest of the world by day 0 or weren't you?
On the issue of aircraft carriers, I disagree. By day 0, people were presenting with symptoms and everyone knew it was a bad disease--they didn't think it was lethal, but they knew it was highly contagious. They knew enough for Iceland to close its borders. Nobody in their right mind would risk an aircraft carrier being out of commission for two weeks (which was the number used in the comic, IIRC). I have no doubt that, if they absolutely needed a personnel change, there would be a rigorous screening process beforehand. The Rash is dangerous and highly contagious, but not invisible. Maybe this wouldn't work for all 10 of the aircraft carriers, but I find it pretty easy to believe that the majority would be able to make it.
As for the small island with the bed and breakfast? That depends on a few things. If it's an extremely popular tourist destination, then yeah, it's pretty much done for. If it's a smaller place that happens to get a few tourists now and then, though, I think it's got a fighting chance. You're assuming that just about everybody were carriers by day 0, which I think is almost certainly wrong. Aino and Kaino came directly from a city (a train station, no less) on day 5, and they were both fine. If a few people visit a small, remote island after day 0, I think there's a fair chance that they wouldn't be sick. The closer to day 0 it is, the more likely they're not carriers; the farther from day 0 it is, the more likely they are to cut off travel. You are right, though, that if even one of them is sick, the whole island is done for. It's definitely far from certain that they'd survive, but I'd give them a much better chance than "All dead. Or trolls."
For, say, entire countries, I agree. if you're not closed off by day 0, then there's not much hope. For remote islands, though, I think it's safe to be a lot more lenient.