If Heater Off means ......... blower Off or your temperature switch is on Cold?
Supposing if blower is on but Temperature switch is on cold and you still get little heated air then this means your valve that supplies radiator coolant to heater is not closing properly. Check to see if your cable is intact. After that if it is and is adjusted correct change your valve if faulty.
Is it normal..... depends on cabin temprature i guess but i dont feel its normal