Your view, dear reader, seems to presuppose that the only reason anyone should care about global warming (or any other problem that will affect future generations) is that one may have (biological?) descendents that might be affected. That presupposition seems false. On the one hand, it's not obvious why I should care more about my distant descendents (e.g., great-great-great-great grandchildren) more than other people who live 100+ years from now. If we care about any other people (i.e., are not egoists in the strictest sense of the term), then it seems we have good reasons to care about (and we have obligations to) lots of living people we don't know at least as much as distant descendents we don't know. If biological relatedness is supposed to support your presupposition, it would suggest that we should care less about our adopted children than biological ones, which seems false. And my relatedness to distant descendents gets cut in half each generation, so after enough generations, I'll be less related to them than, perhaps, I am to you! And should we only care about our friends if they are related to us, or if they can pay us back for any care they give us?
The basic point is that, if you don't want to go whole-hog and accept some form of nihilism or amoralism, then it's likely that under just about any moral theory, you have obligations to people other than your (biological) family and your friends. You likely have obligations to future generations too. And if you don't, then I probably don't either, even though I have children.
Ultimately, I am convinced by Sam Scheffler that we need future generations to give meaning to our lives and and our life projects.
See his NYTimes article here for a summary of the arguments from his book, Death and the Afterlife: http://opinionator.blogs.nytimes.com/2013/09/21/the-importance-of-the-afterlife-seriously/?_php=true&_type=blogs&_r=0