Actually, in a truely libertarian society, no one would give a shit about global warming, since the only person you should be looking out for is yourself, which includes saving money by purchasing the cheapest energy possible.
This type of confusion is the reason you have to separate the issue in two. There are two possible cases:
1) Global warming is not a real problem. In this case, as you say, nobody would give a shit about it because it's not going to hurt them. But there's no reason they should care.
2) Global warming is a real problem. In this case, those individuals who are really looking out for themselves
would give a shit about it because it's going to hurt them.
You can't have it both ways. You can't say the problem is real but that still there's no incentive for anyone to find ways to reduce other people's impact on it.