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.
1) Global warming is not a real problem. In this case, some would believe it is a real problem and others would not. Behavior would be as it is today, minus any regulatory actions to curb it.
2) Global warming is a real problem. In this case, some would believe it is a real problem and others would not. Behavior would be as it is today, minus any regulatory actions to curb it.
3) Global warming is not a real problem, with a solid consensus that it is not a real problem. Behavior would be as it is today, minus any regulatory actions to curb it, plus even less incentive to decrease pollutants, which would inevitably have unsatisfying results.
4) Global warming is a real problem, with a solid consensus that it is a real problem. Behavior would be as it is today, minus any regulatory actions to curb it, with the exception that some fraction of the population voluntarily tries to decrease pollutants, while others take advantage of the decrease in harvested resources to harvest those resources themselves at a lower cost, thus accelerating global warming anyway.