The total meridional heat transport (MHT) is relatively stable across different climates. Nevertheless, the strength of individual processes contributing to the total transport are not stable. Here we investigate the MHT and its main components especially in the atmosphere, in five coupled climate model simulations from the Deep-Time Model Intercomparison Project (DeepMIP). These simulations target the early Eocene climatic optimum, a geological time period with high CO₂ concentrations, analog to the upper range of end-of-century CO₂ projections. Preindustrial and early Eocene simulations, at a range of CO₂ levels are used to quantify the MHT changes in response to both CO₂ and non-CO₂ related forcings. We found that atmospheric poleward heat transport increases with CO₂, while oceanic poleward heat transport decreases. The non-CO₂ boundary conditions cause more MHT toward the South Pole, mainly through an increase in the southward oceanic heat transport. The changes in paleogeography increase the heat transport via transient eddies at the northern mid-latitudes in the Eocene. The Eocene Hadley cells do not transport more heat poleward, but due to the warmer atmosphere, especially the northern cell, circulate more heat in the tropics, than today. The monsoon systems' poleward latent heat transport increases with rising CO₂ concentrations, but this change is counterweighted by the globally smaller Eocene monsoon area. Our results show that the changes in the monsoon systems' latent heat transport is a robust feature of CO₂ warming, which is in line with the currently observed precipitation increase of present day monsoon systems.