Thanks all - to answer a few questions. The electrician has used stranded cable - I'm not sure of the exact gauge but looks like what I'd expect in a 13amp domestic cable. There is actually a second Nest thermostat piggy-backed from the first but only a foot or so away from the first on the other side of an internal wall. If I remove the Nest thermostat from its mounting plate I can feel warmth from the wires to the mounting plate and this heat seems to be confirmed by developments (see later). I looked at the alternative power supply that comes with the Nest thermostat - a wall plug that provides a micro USB connection which says it is "7W 5V DC". So I have used the 8V output from the BG Bell transformer instead of the 12V and as a result the ambient temperature behind the stat has gone from 30C to 25C - so a definite step in the right direction. The unit is using Wifi for signalling back to the Heatlink so I'm guessing the answer is probably to find something that will convert mains voltage to 5V DC. Presumably this must fit in the nest plug (which is no bigger than a standard UK plug ie no wall wart or additional PSU) so hopefully it's doable. I will get googling but if anyone knows of such a thing I'm all ears. Thanks again for all the advice and suggestions, Rob