You said...."When they are off, they use no electricity. The lower you set the temperature, the longer the unit will run, and the more electricity you will use. It is as simple as that. "
Maybe not.......There is a third condition you are ignoring.. An AC can draw 3 times as much current when it is starting then when it is running. So continuously starting and stopping your compressor will result in using significantly more power. Frequetly changing the inside temperature setting will cause the AC to start the compressor and cooling fan many more times then when you leave the AC set at one temperature.
If you are using a heat pump, it is even more important not to keep changing the control temperature. A heat pump is slow to recuperate. That is, it has to run a relatively long time to bring the inside temperature to the set temperature. In addition, the back-up aux. heater is frequently a resistive type heater, that uses a lot of electricity. Sort of like blowing air over a toaster. The aux. heater will typically come into play when the outside temperature is below 32 degrees and/or when the inside temperature is set to more then 3 degrees higher then the actual room temperature.
If you want to save money, replace your AC/heat pump with a unit that has a staged compressor. It will run as a low BTU unit when the outside temperature is mild and as a larger BTU unit when the outside temperature is extreme.
In our area of Florida, my staged heat pump runs as a 1.5 ton unit when the outside temperature is mild and as a 4 ton unit when the temperature is extreme. It typically runs as a 1.5 ton unit 84% of the time. Carrier recently introduced a heat pump that is infinetely varitable. That is, it will run on a wide variety of BTU levels to suit many different outside ambient temperatures. I've been living in Florida for 23 years. I have learned to leave my temperature controller set to 78 degrees in the summer and 72 degrees in the winter, except when I am away for more then 4 or 5 days. When I replaced my single stage heat pump with a two stage heat pump, I saved an average of $65.00 a month on my electric bill over the previous year when I was using a single stage heat pump.
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