Marthe, I've worked on a number of these type units as a Mr. Fix-it for friends and my own systems, so here are some observations and hints:
Your main furnace & A/C evaporator cabinet (I assume in your basement) has a master control circuit board that controls all the logic of starting, stopping and emergency shutdown for both heating and A/C. The controller has automatic delays built-in to prevent damage to the compressor for A/C use, and to prevent your furnace from overheating or exploding in the winter.
Typically, when there's a new start of the system or a restart attempt, there will be about a 3-to-5 minute delay before the compressor will restart and cooling can resume. This safety delay also occurs when power is interrupted accidentally or during a storm.
Often, the new digital thermostats may have delays as well, mainly to prevent false starts because people can be clumsy getting the settings adjusted. Therefore, when you change the setpoint, there is usually a delay before anything changes in the system.
Your thermostat talks to the basement cabinet controller board and that controller commands the outdoor evaporator/compressor unit to start and stop. It also controls the house main circulating fan and the gas burner (or electrical heating elements) in the winter.
Your controller board may also take inputs from a number of safety switches, including low-airflow (due to plugged air filters) along with safety switches for furnace operation.
Typical breaker and disconnect arrangements:
1. Your basement main cabinet (includes the house circulating fan) will be on one 120V breaker in your panel. There's typically also a local lighting-type toggle switch on the side of that cabinet that disconnects that same 120V circuit. For safety reasons, it allows you to conveniently shut your system down when you change the air filters.
2. The compressor (outdoor unit with condenser exhaust fan) will be fed by a two-gang 220V breaker in your panel and usually also has a local pull-out disconnect mounted on the exterior wall next to that unit. On some older systems, that disconnect also contained cartridge fuses.
And yes, your system will not operate with dead batteries in the newfangled thermostat. Good idea to keep a spare around.
Good luck and hope this helps!
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