Q: Could a bad ignition coil cause a lack of heat when turning on the heater?

The ignition coil generally does not have anything to do with the engine’s ability to produce heat when the engine is running properly. The lack of heat you are experiencing may be a result of a clogged heater core. The [heater core]((https://www.yourmechanic.com/services/heater-is-not-working-inspection) is a small radiator like unit that circulates the hot coolant from the engine through the heater core which then uses this warm coolant to heat the inside of the car with the help of the blower motor that blows the warm air through the vents inside the car. The other possibility is that the thermostat may not be allowing the engine to reach a normal operating temperature and since the engine’s warm coolant is the essential source of the heater core supplying heat to the inside of the vehicle, this can impact the warmth of the heat inside the vehicle.

The question of the ignition coils not working properly is a separate issue which may very well place the car into "limp mode." Ignition coils are coated with a varnish-like insulation that becomes brittle over time after being stretched then contracted repeatedly The insulation develops small fractures that open when heated and close when cooled. When open, they allow shorting of coil windings and decrease or eliminate the coil’s ability to function. I would suggest having an expert from YourMechanic come to your location to diagnose your heating and ignition systems.