In my experience, thermostats without a neutral do not function very well!
What a sweeping statement. Most of my thermostats do not have a neutral, I think around 16 through the house, some mechanical, some battery at least one is 12 volt, the use of a neutral can change the slewing range of temperature with mechanical thermostats. It is a bit of a hit and miss system, there is a small heater (anticipator resistor) that can heat the thermostat when switched on, which will cause it to switch off early.
The thermostat I use for beer brewing has an adjustable slewing range of temperature 1-30ºC. And some of the battery powered thermostats have a switch to select 0.5ºC or 1ºC, the Honeywell wireless thermostat my mother had used a mark/space ratio to stop an over shoot, however since she had a modulating boiler, that £100+ thermostat was not suitable for her boiler.
The wall thermostat can be roughly split into three, the modulating which we will forget about for moment, and the on/off which can work in two very different ways.
The old idea was the wall thermostat controlled the room temperature and with my old house, placed in the arch between living and dinning room with an open plan house it worked very well.
However many houses have internal doors, this idea has been with us for some time, and the door prevents or at least reduces the effect of a single wall thermostat for whole house, plus with gas fired boilers, often they can modulate (turn down) so we want to retain this analogue control as much as possible.
The TRV (thermostatic radiator valve) in the main is also analogue, it does not switch on/off, but alters the flow to allow each room if required to be set to a different temperature, electronic heads can even allow times to be set, as to when each room is heated, however unless linked to some form of hub, they have a problem, they can't turn the boiler off, they can turn it down, and then cause it to cycle, but can't turn it off as if they did, they could not turn it on again.
So we need an on/off wall thermostat so on a warm day, it can turn whole boiler off. We really don't want it cycling the boiler, each time the boiler is cycled by an external device, it starts again adjusting its output, so we want a wall thermostat with a large slewing range, and we need to adjust the TRV and lock shield in the room with the wall thermostat so it will allow whole house to get warm before it switches off. If fitted in a room with no alternative heating, including sun through windows, and no outside doors, on a lower floor of course as heat raises, and normally kept cool, then we can omit fitting a TRV.
However in many houses no such room, so we fit the wall thermostat in the hall, so when the front door is opened the TRV will adjust the heat (electronic ones may detect to rapid drop in temperature and it assumes a door or window has been opened, and starts a timer, so TRV turns off for a time first, but then will open wide to reheat the area) so we get a rapid start to reheat, but before it turns off the wall thermostat it slows down, so rest of house can heat up, having the resistor disconnected can actually help with this.
The biggest problem with the wall thermostat is the cooling time for the room, we can adjust heating time with the lock shield valve, but we have no control over cooling time. So a thermostat in the hall, and hall cools slower than living room, and then living room gets cold before heating restarts, real problem with non modulating boilers, but with modulating boilers in heart of winter they should not turn off, only up and down, so the TRV is King at controlling room temperatures.
I have 9 cheap electronic TRV's and 5 mechanical TRV's, and they work well.
but the OP does say:
