Transfer of energy from radiated to conducted

The heated $CO_2$ molecule would have higher Kinetic Energy, from $K.E =frac{3kT}{2}$.

The mean free path of air molecules at STP is about $10^{-7} m$, so simply by colliding with the other molecules the carbon-dioxide molecule would transfer some of that energy.

There would be other mechanisms such as infra-red re-radiation, but the collision process would be quick and transfer energy to the other molecules.

This website has more detail

https://scied.ucar.edu/learning-zone/how-climate-works/carbon-dioxide-absorbs-and-re-emits-infrared-radiation

and says

"Molecules are constantly in motion, colliding with other gas molecules and transferring energy from one molecule to another during collisions. In the more-complex, real-world process, a CO2 molecule would most likely bump into several other gas molecules before re-emitting the infrared photon."