Climate change has received an extensive attention from public opinion in the last couple of years, after being considered for decades as an exclusive scientific debate. Governments and world-wide organizations such as the United Nations are working more than ever on raising and maintaining public awareness toward this global issue. In the present study, we examine and analyze Climate Change conversations in Qatar's Twittersphere, and sense public awareness towards this global and shared problem in general, and its various related topics in particular. Such topics include but are not limited to politics, economy, disasters, energy and sandstorms. To address this concern, we collect and analyze a large dataset of 109 million tweets posted by 98K distinct users living in Qatar -- one of the largest emitters of CO2 worldwide. We use a taxonomy of climate change topics created as part of the United Nations Pulse project to capture the climate change discourse in more than 36K tweets. We also examine which topics people refer to when they discuss climate change, and perform different analysis to understand the temporal dynamics of public interest toward these topics.