I understand exactly where you are coming from.
The issue is a component failure, nothing you have done, and Google are FULLY aware of this problem. The component is like a fuse, and when it gives up users are stuck without heating. The failure is unfortunate, and Google must be really hacked of with this, as they are paying thousands out to rectify the problem. I'm NOT a Google fan, as they take can forever to get some problems solved, but with something like this they should move swiftly!!
Take both of your issues, 24hours later, and not one Google person has stepped in and helped you! Reason being this is a community forum, not the company direct. Why have you not contacted Google Nest direct? I expect the reason being you think this is Google Nest direct?? The best thing to do is ring them, and talk to an agent direct. The phone number is free, and easy to just search in your browser.
The component that has failed inside is an 80p item, and I have repaired many of them. However, Google does has a warranty for 2 years, and should replace the heat link, and probably will.
However, the reason I keep saying to users go back to the retailer, is because here in the UK [assuming you are in the UK] we are lucky and have consumer law on our side, your thermostat set and anything you buy come to that, is covered by the retailer for far longer than a Google warranty.
For a fault like this, I would ring or chat direct to Google Nest, and get the problem solved.
You will now see, a community Google person come and help you out, then they will lock this thread, so you cannot follow on with your replacement experience to explain to others how you got on! Should this not be the case and the thread does not get locked, keep coming back to explain how you get on, and if you have been reimbursed for any cost you have encountered.
Good luck.
