You say when it fires up, if the boiler is working correctly it should turn up/down not on/off. Not quite that simple, but the basic method is the TRV turns down a radiator as the room warms up, the water is either forced through radiators which are still heating rooms, or lifting the by pass valve which means hot water is returned to the boiler, this tells boiler to turn down it's flame height, early units the return water was at its hottest just before the boiler reached its lowest output, however this means when the boiler starts to cycle the unit is hot so heat wasted out of the flue.
So the software has over time become more complex, so when the flame height is at minimum then the return water is at its coolest, one way is to use a different type of thermostat, moving from the old fashion digital (on/off) to a modern analogue one (modulating) these connect to the boiler bus and turn the boiler up/down electrical rather than using the return water.
So you can fit electronic heads to the TRV which tell a hub what heat is required which in turn tells the boiler what to do. Or the other method is to have multi speed fans in the radiators which alter speed according to room temperature.
The simpler systems however have a draw back, the boiler can sense with return water temperature when the rooms are warm enough, however once it switches off, it has no way to sense when to switch back on, one way is to use a variable timer, so if it switches on and the heat is not required then it increases time, and if heat is required it reduces time, this is called anti cycle software, but even this will still fire up boiler every so often over the summer.
So the tried and tested way around the problem, is a wall thermostat, simple off/on, in a room kept cool, down stairs, not alternative heating, and no outside doors. The problem is often there is no such room, so although not ideal the hall is used. However this thermostat is not designed to control the temperature of the home, it is purely to turn off heating as summer comes.
The major problem is for this all to work, the TRV has to be correctly set, and marked * 1, 2, 3, 4, 5, 6 which is not ideal for setting temperature, it would be much easier if it was marked in °C, with electronic heads this is the case, with two sensors one air and one water they auto compensate for the heat from the radiator. They also include timers so each room can be independent.
So reading between the lines the TRV's have not been set correctly and instead the them controlling the temperature the wall thermostat is doing the job.
