I think there is a difference in technical concepts that you are mixing up. What you are talking about is convection cooling. Both compressor based systems and

I think there is a difference in technical concepts that you are mixing up. What you are talking about is convection cooling. Both compressor based systems and peltier coolers need to transfer the removed heat to the environment. This is usually done with big surface areas and potentially fans to produce airflow. In a traditional compressor based system this huge surface area is the radiator in the back and technically it also only "moves the heat" to the surface of that radiator. But give the size of that radiator it will be effective at transfering that heat to the surrounding air. A peltier cooler with a smaller surface area needs a heat sink and or some form of active cooling (airflow, water etc).