While looking on the internet earlier to try and resolve the connectivity, to no avail, I did see there were three or four different brand names with the same stat as I have, probably bulk manufactured somewhere and branded dependant on order.
When I popped the front off, the rear of the unit did feel warm, which isn't surprising seeing as that is where all the electrical stuff happens, maybe that is what is causing the stat to think the air is hotter than it actually is.
As you say though, fiddling with it probably didn't help and it might take a day or so to settle in.
Routers have two channels, 2.4ghz and 5ghz, 2.4 is slower but has long range, 5 is faster with a short range, when you connect via Wifi the equipment connecting typically picks up on the strongest signal, so in my thinking, with the router being in the front room and the stat being in the hall, it should pick up the 2.4ghz, but I will need to disconnect known devices to determine if the stat has picked up the correct channel.
I will keep this thread updated.