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The room thermostat for control of my central heating system is a Siemens RDH10RF wireless unit but I am unhappy with the temperature tolerance provided.
The unit seems to operate to +/- 1degree C of the set temperature, in other words if the controlling temperature is set to 21 degree the heating will continue to operate until 22 degree is reached and only turn back on when the temperature has dropped to 20 degrees. This results in a waste of energy to obtain the upper tripping temperature and a cool room temperature before the system will restart.
Is anyone able to -
1) confirm this tolerance is not typical of wireless room thermostats
2) suggest an alternative wireless unit where tripping temperature will closer reflect the set temperature

No thermostat will control heating without a variation. Because a thermostat works as an on/off switch, the temperature has to fall by at least one degree to trigger the "on" mode. So a stat set at 21 degrees must fall to 20 to activate the boiler.

Conversely, although the thermostat is switching the boiler off when 21 degrees is reached, residual heat in the radiators continues to heat the room above the set temperature.

Unfortunately, this is all perfectly usual for a heating system.

I have a similar problem but in my case hard wired thermostat. I changed the old bi-metal strip type for an electronic type a Horstmann DRT2 Room Thermostat and the data says it has a 0.5 degree difference between on and off but in real terms the air has to move around the device so likely more. My problem is as soon as the fan in the Myson radiator stops blowing warm air out of the radiator it very quickly gets cool.
So I have moved the Myson radiator and fitted a convector type radiator which just sits there full of hot water.
I am sure if I really put my mind to it I could work out a system, but today new systems don't use electric thermostats they use mechanical ones fitted to the radiators. The modern boilers don't just switch on and off but have a variable output and as the return water gets warm the flame height drops and as it cools the flame hight lifts. The electric thermostat is then only there to switch off the system in the summer to stop it having to cycle to test temperature.
The problem is I want to change the temperature through the day. As 6:30 is switches to 16 degrees, I know it will overshoot so it will hit 18 degrees so at 8:30 it is set to 18 degrees in my house this catches the overshoot. At 6pm it changes again to 20 degrees and finally at 11pm it goes to 10 degrees overnight. The radiator thermostats are however just one temperature as a result many including my mother try to use both. However although turning down to 10 degrees overnight works if set just a little lower than radiator temperature the two systems can fight each other.
The scenario seems to be the radiator turns on but before it is fully hot the electric thermostat turns off so the radiator is only warm not hot. However still hot enough to work the radiator thermostat which in turn switches off and this is quicker than design as no water flow. Electric thermostat turns on but no water flows to begin with as radiator still off. Net result the room cycles hot and cold as the two thermostats fight for control. According to distance between the radiator and thermostat this could be reversed but net result the same bigger temperature swings.
Tried opening the radiator thermostats full open but this does not work. When they are set they stop the hot water returning to boiler through that radiator and forces it through other cold ones. Once all radiators are hot then the bypass valve opens allowing hot water to return to boiler. This in turn switch down and finally off the boiler.
As summer approaches the boiler has a memory. Anti-cycle it's called. It switches on and after a delay checks the temperature of return water. If it hot then it increases the time before it tries again. If cold it decreases the time before it tries again. But it has no way to know that it's going to be a nice day and it may get house to hot. So by putting a thermostat to catch the morning sun this can then stop the system firing up when it is likely to be a warm day.
So the modern electric thermostat has two roles.
1) To reduce the overnight temperature but not switch completely off.
2) To stop cycling on hot days.
The rest is done by the ones on the radiators.
With the old system before radiator thermostatic valves the distance between radiator and thermostat could make a huge difference. The closer it is then shorter the on/off times the further away the longer the on/off times. However it would also effect the temperature of the room and instead of setting at 20 degrees one may need to set at 22 degrees and as summer approaches one has to slowly reduce the temperature. At one time I had a huge problem trying to get temperature correct. Found when thermostat was fitted a hole had been drilled into garage to wire to boiler. When wind was in wrong direction a cold draft through this hole stopped the thermostat turning off. To a lesser degree mounting a thermostat on any outside wall can mess it up.