In air conditioning units, the temperature settings on the cold mode and warm mode represent different functions and strategies for temperature control. The difference in the perceived temperature between 20°C on the cold mode and 20°C on the warm mode is primarily due to the way these modes operate and the desired outcomes they aim to achieve.
When an air conditioner is set to the cold mode, it cools down the air in the room by removing heat from it. The air conditioner's compressor works to lower the temperature below the ambient temperature, typically set by the user. So, if you set it to 20°C in cold mode, the air conditioner will work to lower the temperature in the room to reach that set point. As a result, the air that is blown out by the air conditioner will be colder than the ambient temperature, making the room feel cool.
On the other hand, when the air conditioner is set to the warm mode, it operates differently. In this mode, the air conditioner's compressor works to heat the air in the room. It extracts heat from the outside environment and transfers it to the indoor air. So, if you set the air conditioner to 20°C in warm mode, it will aim to raise the room temperature to that set point. The air blown out by the air conditioner will be warmer than the ambient temperature to achieve the desired warming effect.
Therefore, although both modes may have the same temperature setting, the way the air conditioner operates in each mode results in different perceived temperatures. In cold mode, the air conditioner lowers the temperature below the set point, while in warm mode, it raises the temperature above the set point.