Non-proportional control in which the controlled process input is either fully ON or fully OFF depending on whether the temperature is above or below the control point deadband.
why specially you choose temp as process parameter ? on-off control can work with any kind of process or measuring parameters . for example if we need to close inlet valve when level reach predefined level so we can used on-off control.
also P only controller with infinity gain could be used as on-off controller
no specific reason, its a general house hold appliance example which we study in our books.