I'm wondering how the car knows the temp isn't comfortable. Take it to a dealer. You could need a thermostat, heater control valve, heater core, or a sensor. Start/stop won't engage unless the coolant's in a certain temperature range. Sounds like the ECU thinks the car is too cold.
You have 2 temperature blend doors, one for each side of the car. The one blowing cold air is stuck or inoperative. If you're in warranty let the dealer fix it. I don't remember if it sets a code but it's not needed since you have the problem. When I have a problem like this I make sure it's doing it when I pull into the dealer and don't shut off the car until at least the service advisor observes it, just in case. If you have VCDS you can do a scan for kicks to see if there's a fault set, just don't do anything else.