Q: Heater core or thermostat

If the engine temperature, as measured on the dash gauge, does not reaching the normal operating range within "roughly" 5 miles or so of driving, then a possibility is the cooling system thermostat is stuck open. Among other things, a stuck open thermostat will "somewhat" reduce the available heat to the cabin but, worse, will degrade the fuel efficiency of the engine. If the engine is reaching the normal operating temperature range within a reasonable interval, keeping in mind that cold weather will slightly increase that interval, and yet you have inadequate cabin heat, that could mean that the heater control valve is not fully open, the HVAC ducting is blocked, and/or the heater core is partially plugged. There are other possibilities, for example, check the engine coolant level (but, for safety reasons, only when the car is absolutely STONE COLD). If needed, you can request a thermostat replacement and/or a diagnostic on the inadequate cabin heat issue. Please let us know how we can best assist you further and, as well, if you have follow up questions.