Effective climate change mitigation is a social dilemma: the benefits are shared collectively but the costs are often private. To solve this dilemma, we argue that we must pay close attention to the nature and workings of human cooperation. We review three social cognition mechanisms that regulate cooperation: norm detection, reputation management and fairness computation. We show that each of these cognitive mechanisms can stand in the way of pro-environmental behaviours and limit the impact of environmental policies. At the same time, the very same mechanisms can be leveraged as powerful solutions for an effective climate change mitigation.