One thing you said struck with me, that there was nobody living next door. In our three bed semi - there was only (if I remember correctly) block on edge between us and our neighbour. If this is the case here, then the adjoining wall has no insulation in it. It therefore will act as a sponge soaking in heat and radiating it in to the cold house next door.
In our house, every room, except the bathroom and one bedroom, had one (long) wall that adjoined the neighbours house.
To test this theory, can you get a couple of thermometers, close the doors and check if the rooms that are adjoining next door are colder than the rooms that are not.
If it turns out to be the case, then you have a problem, until someone moves in next door and turns on the heat.