Even with the success of representing the structure of the Hadley circulation, the theoretical model shows limitations compared with observation due to missing of interactions with other regions, especially mid-latitudes. Here, we extend the original model to include the influence of mid-latitude large-scale atmospheric dynamics. The large-scale atmospheric dynamics in mid-latitudes is represented by the planetary-scale heat equation with a parameterized poleward heat flux induced by synoptic eddies. The energy flux balance inside the cell includes the poleward heat flux at the poleward edge of the cell controlled by the baroclinic instability of sub-tropical jets. Theoretical solutions suggest that global warming, which can reduce the baroclinicity in mid-latitudes, can lead to the poleward expansion of the Hadley cell due to the update of the energy flux balance inside the Hadley cell.