Climate change affects the effectiveness of monetary policy, particularly in maintaining price stability. In a two-period theoretical model with heterogeneous agents, monetary policy and climate externalities, we establish that a trade-off exists between climate change and inflation. In addition, lower interest rates for green investments enhance economic growth and aggregate social welfare when carbon tax is not at the optimal level. Our analysis suggests that green monetary policy and carbon emission taxes are complementary rather than substitutes. Our findings provide policy implications for balancing climate change mitigation and economic stability for the South African Reserve Bank.