Yes the nest, or any thermostat will work fine in a bedroom, if the heating system is properly balanced.
The old idea of it must be in the coldest room is wrong. The thermostat should be in a room with a radiator which does not have a thermostatic valve on it, otherwise you'll hav etwo thermostats working against each other.
All other radiators should be balanced against the 'control' room so that every room heats up in line with that room.
Then is variations in temperature are required in each room they can be achieved by using the thermostatic valves on the radiators, but overall the system will heat up uniformly.
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The thermostat should not be in the coldest room, that will cause all of the other rooms to be overheated.
It depends how the thermostat is used, there are two ways to use a thermostat, in my old open plan house the thermostat was near the arch between living and dinning room and it worked well, upstairs could over heat if doors left open to bedrooms, but use of TRV on bedroom radiators reduced this problem.
In this house the wall thermostat is in the hall, and in theory for it to work the hall TRV needs linking to the wall thermostat, however thermals in the hall don't carry the heat to the wall thermostat very well, so in real terms the TRV has to be set lower than the wall thermostat, not quite worked out why, but the wall thermostat always shows a higher temperature to the TRV.
At moment target 17°C current 16°C, but wall thermostat target 18°C and current 18.5°C so within the hall the temperature varies from 16°C to 18.5°C so to get the wall thermostat to turn on the boiler the TRV schedule needs to be set around 2°C lower on the TRV to the wall thermostat.
Big point is if using a programmable wall thermostat then the TRV also needs to be programmable.
But first look at how the boiler is controlled, with gas in the main the boiler can be modulated, that is turned down, so to stop the hysteresis (sine wave of temperature) everything is analogue, the TRV slowly closes as the room warms up, this causes the by-pass valve to slowly lift, and more and more non cooled water to return to the boiler, which in turn causes the boiler to reduce output, and the reverse as room cools.
However there is a problem, as the weather improves the boiler reaches minimum output, so at that point it has to cycle off/on. And as the weather improves further the boiler will continue to cycle all through the summer, so the way to stop the cycling is the wall thermostat, which only actually turns off the heating in the summer. In the winter the wall thermostat does nothing.
There is another way, still analogue, this time the thermostat connects to the boiler ebus, OpenTherm is the most used system, this allows different makes to work with each other, but some makes don't allow third party thermostats to be used.
And now to another method, Hive have a "heat on demand" system, not sure how well it works, but the idea seems good, the TRV head sends a signal to the wall thermostat which in turn runs the boiler for 1/2 hour each time it gets a demand, this means the return water temperature controls boiler, and the thermostat keeps boiler running if any linked TRV head says it wants heat, so in this case it does not matter what room the thermostat is placed in.
There are other systems, EvoHome is about the best know, it calls it a wall thermostat, but really it's a hub and each room is individually controlled.
As you can see from what I have said, the main control is the TRV not the wall thermostat, the older wax TRV heads are a bit useless *123456 does not really help setting the temperature, nor does it help when not programmable, however the TRV heads that link to the wall thermostat are around £50 each, however stand alone units like the eQ-3 and Terrier i30 can be found as low as £10 each, I got some bluetooth versions of the eQ-3 at £15 each.
So theory for me was 4 Energenie MiHome programmable TRV heads linked to follow the Nest gen 3 thermostat, and 5 bluetooth eQ-3 heads in bedrooms and kitchen. However two problems, one the heads often don't follow Nest, some times it works, but not all the time, and the TRV head needs setting 2°C below wall thermostat, so I could have used eQ-3 TRV heads for all radiators, and saved myself £140.
I have talked about a modulating gas boiler, oil boilers in the main don't modulate, they only switch off/on, it's called a mark/space ratio, and the radiator needs to hold more water so it holds the heat for longer again to reduce the hysteresis.
There are also special radiators, the fan assisted radiator does not have a TRV instead it turns the fan off/on, in some cases the fan is multi-speed the advantage is you don't get cold spots like I have in my hall as air circulated, they are a lot smaller, and can fit in the plinth of kitchen units, however you can hear the fan running, and they cool down and heat up quickly, so within minutes of boiler switching off, you feel it go cold.
So to original question, yes Nest gen 3 will work with a S plan and it can be configured in many different ways both mark/space and Opentherm control.