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I haven't seriously studied Friedman since I was an undergrad at SMU where I majored in economics and I have no personal knowledge what, if anything, he wrote on the subject. The SUM economics department was heavily laced with Chicago school profs, however, so I can perhaps make an educated guess on how you can reconcile a Chicago school belief with a moral view on global warming.
Those who pollute and cause global warming are imposing external costs on the rest of society. I think it is consistent with at least some brands of free market economics to acknowledge that one of the legitimate roles of government is to internalize external costs. The Coase theorem (named after Ronald Coase who certainly fits in the Chicago mold) suggests that absent transaction costs, it makes not difference who we place the burden on to pay the external costs, that the parties will nevertheless negotiate the most efficient outcome. Of course, in the real world there are transactions costs, so you cannot ignore them. Therefore an enlightened Chicago school disciple who believes that the government should internalize external costs would look and see which party has the lowest transactions costs to fix the problems. Here that is the party creating the pollution. Therefore, one would adopt regulations having that person mitigate the deleterious effects of their polluting activity.
However, I do suspect that rather than mandating a specific method of mitigation, a Chicago school solution would allow the polluter to choose from a range of mitigation options (e.g. quit polluting, install pollution reducing equipment, buy out another polluting firm, plant a million trees, buy a rain forest and protect it from being cut down, etc.).
An interesting issue that you raise, and one that has, I suspect, been written on more thoroughly and more thoughtfully that I have done here. But quite interesting.