Generally, no. The heater core usually has a direct line from the water pump, if the coolant was so low as to not circulate through the heater core your engine would overheat. Most likely a clogged heater core. Rust and sediment build up in the coolant system over time and cam clog the narrow channels in a heater core, which looks like a smaller version of your radiator. A reverse flush can sometimes clear the core out, but a severe case may require replacement. Any auto parts store can sell you a flush kit for about $10. I've used the prestone one with no problems, since the core may be really clogged, get the system cleaner bottle as well to ensure you get the most crud out possible. Follow all the directions on the kit, and cleaner, make sure you are using compatible antifreeze when you refill. DO not open any part of the cooling system with a hot engine (more than warm to the touch). Doing that can cause severe burns, blindness, or worse if the antifreeze in the engine starts to boil off violently.
engine not warm, low coolant, or stuck thermostat
Sounds like it is low on coolant.
Insufficient amount of coolant or thermostat not opening
Test the coolant freeze point to be sure the coolant is not freezing up when it is cold outside.
if its blowing, but not blowing cold its low on coolant. it takes r134a.
low on coolant, dash control, blend door actuator are places to start
Check your antifreeze or cooling level this happened to me.
You have run out of coolant, or the heater matrix is blocked.
The heater bypass valve is not fully closing, or leaking hot coolant into the heat exchanger.
Because you are low on Coolant
Low coolant, bad coolant, blockage in the coolant line, bad heater core or element, bad thermostat
Sounds like low coolant or air in the cooling system