Yes - if your heating is not controlled by a thermostat. However, if you have a thermostat, it will cut out the heating at the same temperature, so you may not notice the difference in the room with the thermostat.
However, you should find that the temperature in other parts of your house improves, for example, the small bedroom on the corner. With CWI, you should find that the house holds its temperature for longer; therefore the time between heating cycles may be longer. The result should be a more even temperature throughout the house and a reduced fuel bill.