Increasing atmospheric carbon dioxide (CO2) is expected to be the main factor of global warming. The relation between CO2 concentrations and surface air temperature (SAT) has been found related to Rossby waves based on a multi-layer complex network approach. However, the significant relations between CO2 and SAT occur in the South Hemisphere that is not that much influenced by human activities may offer not enough information to formulate targeted carbon reduction policies. Here, we address it by removing the effects of the Rossby waves to reconstruct CO2 concentrations and SAT multi-layer complex network. We uncover that the CO2 concentrations are strongly associated with the surrounding SAT regions. The influential regions of CO2 on SAT occur over eastern Asia, West Asia, North Africa, the coast of North American, and Western Europe. It is shown that CO2 over Siberia in phase with the SAT variability in eastern East Asia. Indeed, CO2 concentration variability is causing effects on the recent warming of SAT in some middle latitude regions. Furthermore, sensitive parameters that CO2 impacts SAT of top 15 carbon emissions countries have been identified. These countries are significantly responsible for global warming, giving implications for carbon emissions reductions. The methodology and results presented here not only facilitate further research in regions of increased sensitivity to the warming resulting from CO2 concentrations but also can formulate strategies and countermeasures for carbon emission and carbon reduction.