There are 3 possibilities. One, your thermostat is set to cold air or your vent setting is set to allow outside air.
Two, the control valve to the heater core is stuck, and not allowing the hot water to enter the core, so the core remains cold.
Three, the water in your vehicle's radiator is low, and not allowing enough hot water to enter the core.
My suggestion is to be sure the radiator is full. Be sure the car's engine is completely cooled before opening the cap.
Your cooling system is empty of coolant and you must have a large leak somewhere.
Call a heating specialist. Heaters are too dangerous for amateurs to fool with. There is danger of fire and, in the case of gas, asphyxiation if they are not properly repaired and adjusted.
One reason your home electric heater is blowing cold air is the heating elements are burned out. A bad thermostat may also be the problem.
There are many reasons that the cars heating system may alternate between blowing hot and cold air. Some common causes of this include the heater core and air pockets in the coolant.
check the coolant level, or, possible stuck thermostat.
This is caused by low coolant levels in most instances.
No, there is no blower or duct work. You can't chill the water in the heating system and get cold air out of it.
The electric heating elements are probably turned on.
Over-obvious answer? Your radiator, or one of your radiator hoses, leaks - badly.
It is likely you have a heat pump. A type of air conditioning system which heats as well as cools. If there is cold air coming from the outdoor fan, you are in the heating mode. If you are calling for cooling at the thermostat, and there is cold air coming off the fan from the outdoor coil, there is a problem with likely the low voltage wiring.
It's probably the radiator. Make sure there's enough coolant in the radiator.
That is exactly how a heat pump works in heating mode are you sure it's not a heat pump?