Connecting a NEST thermostat to a FON access point

Hello

I've just fitted a NEST (V2) system in a property that does not yet have any tenant so no phone/internet line yet. There is, however, a BT FON signal from a neighbour.
https://nest.com/uk/#meet-the-nest-learning-thermostat
In my house (200 miles away), I am using BT Broadband so have access to the FON system, so Ideally I'd like to control the heating over the internet, so I guess that I'd need to 'bridge' the neighbours wi-fi to enable the device to access the internet.

I have a loft full of bits bought for various projects - I have a couple of TP-link Nano routers and an old Raspberry Pi, so just want to make sure I use up some IT jumble, I can't justify buying any more wires.

Thanks in advance
Jerry

https://gist.github.com/sscarduzio/05ed0b41d6234530d724

did it work? I have tried the same using a netgear travel router but found it disconnects after a day or so and need a manual reconnect

So plug it into a timer plug and have it switch off and on every 12 hours

You really want one of those in your house (and by inference, someone elses' home?) https://www.blackhat.com/docs/us-14/materials/us-14-...
Even if it remains' uncompromised by others, it's still pumping data to Google. There could be an argument that by installing In a property intended to be used by others, you are breaching the confidentiality of their data - maybe even 'spying' if you view their usage and occupation times.