Can heat pumps be turned off?

It's not recommended to turn off your heat pump. There should be no need to turn off a heat pump, as the thermostats within the house maintain a certain temperature throughout the house. 

When the room or 'zone' reaches the required temperature, the heat pump will go into standby mode (as long as the demand for hot water is also met). If you feel the house is too warm, you can turn down the thermostat for the room or 'zone'.