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Climate change is, perhaps, the most important of challenges currently facing humankind, with the potential to have health and welfare implications by imposing a sizeable aggregate risk to the economy. Given this, and in the wake of an ever-burgeoning literature on the nexus between climate change and economic growth, we develop an overlapping generations endogenous growth model characterized by climate change, with the latter being specified as a fraction of output lost due to changes in temperature anomalies. We show that growth dynamics arise in this model when changes in temperature anomalies are a positive function of current economic growth, i.e., considered to be endogenous unlike existing theoretical models on this topic, with this theoretical specification motivated through extensive empirical analyses involving 167 countries over a long span of historical data covering 1851 to 2018. In particular, two distinct oscillatory growth dynamics emerge: one convergent and the other divergent, contingent on the strength of the response of global warming, i.e., changes in temperature anomalies to current economic growth. Our theoretical results suggest that policymakers should be cognizant that unless economic growth is “green”, rapid global warming can put economies in a fluctuating, divergent, balanced growth.