You could have a problem with your thermostat in the car.
A leaking heater core will cause the engine to overheat because the coolant is leaking out.
the heater core is leaking
Not very well.
the heater of your car does not only work when the car is in motion. it only works when the engine is started. you don't have a heater in your car like you do your home. the heat that you feel when you turn on your heater in your car is produced by the engine. and there for if your car is not on then you will not receive any heat. some cars take longer than others to "heat up".
You may smell coolant when the ac is running but a leak in the heater core won't cause the ac not to work.
have you checked the fuses? if so, maybe the heater core needs replacing
well you could just turn the heater off heater blower ---- If it is a car heater then check your coolant level. the heater is driven off a heat converter that is fed by the radiator system. When the coolant fails to pump round the radiator system the car internal heater doesn't work. Driving without coolant in the system will result in the engine overheating and seizing.
engine thermostat, fan motor,or fuse.