We introduce a framework to analyze the conversation between two competing groups of Twitter users, one who believe in the anthropogenic causes of climate change (Believers) and a second who are skeptical (Disbelievers). As a case study, we use Climate Change related tweets during the United Nation's (UN) Climate Change Conference - COP24 (2018), Katowice, Poland. We find that both Disbelievers and Believers talk within their group more than with the other group; this is more so the case for Disbelievers than for Believers. The Disbeliever messages focused more on attacking those personalities that believe in the anthropogenic causes of climate change. On the other hand, Believer messages focused on calls to combat climate change. We find that in both Disbelievers and Believers bot-like accounts were equally active and that unlike Believers, Disbelievers get their news from a concentrated number of news sources.