I believe it’s less about heat dissipation than about adiabatic expansion - where air as it expands does ‘work’ and loses heat.
The heat coming (as far as the air is concerned) mainly from the ground sounds like a good point, but IIRC the temperature at altitude follows the expected curve for adiabatic expansion given the pressure change, so I think that heat-entry-point-effect must be much less significant except close to the ground.
Come to think of it, most heat loss from the earth must be from infra red, which will also come from the opaque ground much more than from the air.