Is there a sensor that limits the energy input when there is already heat in the unit?
Yes, the input control is actually a thermostat which sets the maximum temperature that the thermal blocks inside the heater will be charged to overnight. So long as the night-rate power supply (usually 7 hours) is on for long enough to attain full temperature, for any given input setting the blocks will charge to the set temperature by morning, regardless of whether they started cold or were already partially warm from the day before. Obviously if they start from cold it will take more energy to raise them to the set temperature than if they are already slightly warm, but you won't "overcharge" and lose the excess.
The lack of precise control and the way that you really need to predict how much heat you will need for the next day is one of the major drawbacks of night-storage heating (and of course, predicting what's needed for the next day is always a hit-and-miss affair in the British climate, especially at this time of the year when it's so changeable).
The main problem is making sure you have enough heat stored in the blocks to last you right through to the next night. You'll find that if you set the input control on the low side but still leave the output set high, you'll have used most of the heat by the time you need it most the following evening.
If you are trying to economize by keeping the overnight charge as low as possible, you also need to set the output control down to make sure that the stored heat will last you through the day.
