If you have two samples of air then add additional carbon dioxide to one of them and heat them up.
- Does the one with extra carbon dioxide increase in temperature faster?
- Does the sample with extra carbon dioxide retain its heat longer?
If you just add $CO_2$ to a sample, the energy required to heat it will increase because there is more mass there. You have to heat the new $CO_2$ as well as the old sample. Then if heat is removed from the mixture, it will cool more slowly for the same reason. If you are thinking in terms of this with reference to the increase in $CO_2$ in the atmosphere, it is a trivial effect as we are talking about changes in the $100$ ppm area.
If you have a constant mass of air and increase the fraction of $CO_2$ relative to nitrogen/oxygen, the heat capacity of $CO_2$ is about $37$ J/mol at $15^\circ$ C compared to nitrogen at $29$ J/mol. Since $CO_2$ has a molecular weight of $44$ compared to $28$ for nitrogen, the lower heat capacity per gram of $CO_2$ will lower the heat capacity of the mix.