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I think the original question as I understand is valid and representative of healthy curiosity, but I think the answer could be more tailored to comprehensive understanding if there is a secondary reason behind asking.
Peter7307 is correct (except air is cooled at the evaporator in the heater box; the condenser is up by the radiator and gets HOT). Cars with A/C have two heat exchangers in the HVAC box; an evaporator and a heater core. From there I'm aware of two different ways to control temperature that may be used separately and/or together. Some vehicles have a shutoff valve in the coolant line feeding the heater core that will stop the flow of hot coolant when no warming of the air is desired. Other vehicles have a "blend door" that controls the flow of air between the blower and the vents and allows varying proportions of air to flow over the heater core by changing position of a flap in the ductwork. AFAIK both could be easily used together.
The cycling of the A/C compressor is based on the refrigerant pressure. When running fully cold with a low blower speed the evaporator will get very cold as there is little air blowing over it to warm it up. When this happens the refrigerant regains less pressure after passing through the evaporator, decreasing the pressure on the low side of the compressor. Some systems have a low-pressure cycle switch that shuts off the compressor to prevent freeze-up until the low-side pressure increases (which will happen as the evaporator warms). I'm not sure if many vehicles do this, but one could detect an increase in high side pressure that will correspond with the same events as the decrease in low-side pressure and control the compressor in that way.
To improve fuel economy while using air conditioning the goal should be to maintain the coldest evaporator possible. Operating the ventilation system in recirculation mode allows the A/C to chill already cooler air from inside the car to keep the car cool while operating the compressor less. Using as low a blower speed as you are comfortable with helps as well. At night, in the shade, or when it isn't too hot outside you may notice that in recirc mode at low fan speed it still gets too cold. Rather than cooling outside air or turning up the temperature to warm the air with engine coolant you should turn off the compressor if your vehicle allows you independent control of the compressor (my truck has a snowflake button). When it begins to warm up again you can turn it back on.
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