Nice.
What you could do about the charging issue, is to use a LM2596 module (very cheap on eBay). These accept a wide input range, and the output can be adjusted.
You could use an old 12V adapter (old router or so) and wire it to the LM2596. Then connect some load (small 6V bicycle lightbulb or something) at the other end of the cable (at the thermostat side), and adjust the output until you get a nice 5V out of it.
I think that will solve the issue of the battery draining slowly

Be sure to watch the voltage carefully when adjusting, you don't want to blow up your tablet!
Or put 12V on the wire, and in the wall socket ('inbouwdoos') put a small 12V car cigarette lighter model charger... That way the 12V > 5V conversion is done at the end of the cable and the voltage drop will be gone.
This night i tried the 'RedEye Stay Awake (free)' app, but the tablet didn't wake up. I also couldn't ping it. As soon as i pushed the powerbutton on the tablet, so it woke up, it began reacting to pings...
Now going to try this one:
https://play.google.com/store/apps/deta ... wakelocker and the first test seems to work. Without the app, when i locked the tablet, i couldn't ping it anymore after a few minutes. With the app enabled, i can still ping it when the screen is off. Seems promising

I am not active on this forum anymore.