This article introduces within the DICE Model a new class of consumers with the political or philosophical opinion of "degrowth", so-called deep green consumers (DGC), whose discount rate will endogenously decrease with the economic growth. A new utility function is assumed, using the Ramsey equation, to compute the social discount rate (SDR) in this new way. New paths of consumption and greenhouse gases (GHGs) emissions thus arise for both this social rate time of pure preference and the absolute value of the elasticity of intertemporal substitution of the consumption. In this framework, the SDR is a decreasing function with respect to the share of DGC in the total population. The integral of intertemporal utility proves an increasing function with respect to it. This article assesses the impact of an increase in the share of DGC in the population and shows that, under a certain threshold of DGC around 40%, no significant difference in the temperature decrease before 2100 is found. Above this threshold, the trend of increasing temperatures is inverted, within a time frame of one century: A share of 50% of DGC shows a peak for temperature in 2120, with an increase of +3°C., below Nordhaus' optimal path. These assessments show that changes in public opinion, such as the emerging movement in favor of reduced material consumption, or even degrowth, could lead to significant effects in favor of the climate when reaching a certain threshold. This is due to the inertia of both the natural climate systems and capital investment, arguing for strong complementary economic policy measures to reduce GHGs emissions, in addition to preference changes.