AC is automatically ON in AUTO climate control?

Not quite right. The 12 V battery always runs the climate control fan regardless of the mode.
The HV hybrid battery runs the AC compressor but has no direct involvement with heat.......except on a model that has a "heat pump".

 

You can run the heat or ac all night if the car is in ready mode.


iPhone ?

 

It's not as clean of a separation as you might think.

The 12v battery operates the control logic, sensors and the forced air blower for BOTH heat and a/c systems. The gas engine supplies the raw heat in the form of hot engine coolant. The air conditioner compressor operates from the high voltage hybrid electric system.

At the end of the day, you need everything (12v, gas engine and hybrid battery) operating properly to get HVAC.

Keep the car in READY mode and you'll have fully controlled climate for as long as you have gasoline. Shut down to accessory mode and the car can only circulate air, and then only for a few minutes.

 

... and when in READY (as you will be, for the useful stuff to happen), it really isn't the 12 volt battery that's operating anything. All of the 12 volt parts of the system are getting their power then from the DC/DC converter, which produces 12 volts from the higher voltage of the traction system. In those conditions, the 12 volt battery is a recipient of power, rather than a supplier.