The reason heating thermostats have anticipators is to:

Heating thermostats are equipped with anticipators primarily to reduce overshoot. When a thermostat senses the temperature in a space, it not only reacts to the current temperature but also anticipates changes based on the heating system's behavior.

The anticipator works by monitoring the heating cycles and predicting when the desired temperature will be reached. By adjusting the operation of the furnace slightly before the set temperature is achieved, the anticipator helps prevent the temperature from exceeding the desired level. This mechanism ensures that the space does not become excessively hot, leading to a more stable and comfortable environment.

In practice, if a thermostat activates the heating system and allows it to run until the desired temperature is met, it could cause the room temperature to rise too high, resulting in "overshoot." The anticipator mitigates this effect by turning off the heating earlier, thus enhancing temperature control and comfort within the space.