As part of the service, this controller gives you the option to send commands through an app, or by sending SMS (the device comes with a SIM card and gets its own mobile number). The commands would allow you to ask if the heating is running or not, to turn the heating on or off, and so on.
I first implemented the SMS interface with Twilio, but then found that the number of texts you can send to the device is capped. I don't remember what was the monthly allowance, but I reached it in a few days after querying the device every 15 minutes or so 24/7.
I then found a project on GitHub with the reverse-engineered API that the phone app used to send commands. So I then reimplemented the command logic using this API to be able to talk to the controller without limitations.
I'm not familiar with the Nest devices, but I'd suggest you do a search on GitHub to see if someone figured how to reverse-engineer its API.