You said: <blockquote cite="…
You said:
"The auto start-stop has a sensor to determine if the ambient temperature outside the vehicle exceeds the temperature inside. If it is, the car engine will not shut off. The same is true in the winter. The car will stay running if the outside temperature is colder than the cabin."
According to this, it only works when ambient temperature and cabin temperature are equal. I think you were given some misinformation.