It does both. Originally warm air heating thermostats did simply switch the burner off, then the fan ran for a couple of minutes to cool the heater before that stopped too. In practice, the occupants could feel hot when the warm air was blowing and then cold when it switched off.
As an effort to overcome this, 'thermista-stat' control was introduced. [aka Johnson & Starley Modairflow] As the property warms up, the fan speed is automatically reduced and the burner fires intermittently; the idea being that the heat output would reduce gradually and then run at a level that would maintain the set temperature, thus avoiding the hot / cold feeling created by the original designs that simply switched from max output to off, with nothing in between.
To find the correct setting for your home normally try setting it to 5 to start with, then make gradual adjustments up or down until a comfortable level is maintained. Once a comfortable setting is achieved, the dial should be left in that position, and the heater will adjust its output accordingly. If it's cold, it will start off with maximum fan speed and burner output, reducing down gradually until the comfortable temperature is reached and maintained.
During the milder weather, the heater will still turn off completely as even on the minimum output it would provide more heat than is required.
