Most thermostats are a simple on / off switch. They simply turn the heating 'on' and 'off' that's all they do. When the room in which they are located reaches the set point, off goes the heating. So, in your case swapping the thermostat won't change anything. When the lounge where the stat [Nest, Wiser, Hive, et al] is located reaches the set temperature the heating will still go off.
The problem is either with the design of the system, the thermostat is simply located in the wrong place or as muggles says the system needs balancing to distribute the heat more evenly.
Here's a guide as to where the thermostat should be positioned:
1. The room thermostat should be in a room that is not effected by other sources of heat such as an open fire, cooking equipment, or direct sunlight etc. It should not be somewhere drafty or too close to a window, especially if it's one that is opened in the winter.
2. It should be in a cool room, ideally the last room to warm up. That way the other rooms will be warm enough, (but not overheated if fitted with TRV’s) before the room thermostat switches the entire heating system off. [To achieve this, sometimes it may involve downsizing a radiator in the room where the room stat is located]
3. The radiator in the room with the thermostat installed should not have a TRV fitted. Otherwise the TRV could interfere with the operation of the room thermostat and prevent it from working properly.
4. The thermostat should be mounted about 1.5 metres from the floor, and not close to, or above a radiator.
5. Preferably it should not be on an outside wall, (although if the property has well insulated walls, this is not quite so crucial.)
6. It should be in an area where air can circulate easily, not in a corner, or hidden behind curtains, or furniture.