Dead simple. Cracked it open, chucked an ESP32 in there connected to the soft power button, and to the “machine is on” indicator on the display, which was conveniently on its own pin. No need for any thermal protection cleverness as the machine does that itself.
Now I just turn it back on when I’m heading home, and no longer have to wait for the pot to warm up again.
I then decided to stop using the “make coffee at time” functionality baked into the machine, as the kid gets up when the kid gets up, and the machine would either start early and wake her, or she’d get up before it and I’d have to go start it. Now, she opens her bedroom door, I get “kid is awake” alert on my phone, and the machine brews the coffee.