A growing body of literature proposes a climate-oriented monetary and financial policy for Central Banks (CBs). However, other literature defends a market-neutral monetary policy to keep CB independence and avoid addressing other than conventional objectives. However, if the CBs’ market-neutral policy is only targeting inflation rates and employment, it could amplify the macro impacts of negative economic externalities, while also neglecting positive externalities in the long-run. Even if climate-related policy goals appear advisable, the actions of CBs reveal significant delayed impacts on macro and climate-risk variables. We propose a non-linear dynamic macro model of finite horizon with multiple targets, including macro imbalances and climate risks arising from a trend in carbon emissions. This non-stationary emission dynamic has feedback effects on stationary and non-stationary macro variables and the multiple (possibly conflicting) objectives of the CBs. In this context, we first explore to what extent CBs can impact emission trends with and without delays. Second, given the mix of stationary and non-stationary dynamic variables, we explore the responses to policy and economic and financial shocks using a mixed Vector Error Correction Model (VECM) with stationary and non-stationary variables. Third, in the face of multiple objectives—and macroeconomic concerns that CBs face—we are motivated by Kaya and Maurer (2023) to construct a Pareto front that introduces weights for the multiple objectives and permits target prioritization.