First thing, your wife can just tap on the blank center screen , and the car will wake up again.
There are a few different ways to keep climate on for your passenger while you get out.
1. Before leaving the car, tap on climate control, and choose the "Keep" climate on, this will keep climate on, but will dock the doors after you walk away. If passenger opens the door without unlocking the car first, car alarm will go off btw.
2. Camp mode, this mode will keep climate on, and car alarm off. And it will keep the car unlocked, unless you lock it yourself via the app.
3 Dog mode as Herb suggested, only issue is your passenger won't be able to use the touch screen at all, and can not open the doors either (it's to prevent pets from accidently press on stuff). Your wife may be slightly unhappy.