We've already blown past the warming targets set by the Paris climate agreement, study finds

Are there mathematical models with explanatory notations that delineate the effects of exceeding the Paris climate agreement green house gas emissions? If so I would appreciate links/references to such models. The question I'm trying to resolve: Is the Earth in a natural cooling cycle state which is being impacted/slowed by man made green house gas induced warming? The follow-on question is: How do we keep lights on, heat and cooling available, and economic activity functioning while reducing green house gas emissions without producing scarcities of goods and services required for living?
 

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