Only cold air and only thru defrost vents

What is your question?

The actuator on passenger side under glove box moves when I turn temp knob but air stays ice cold. I can turn into off but when i have it set to blow out any vent it's still only like ac cooled air coming from defroster. Both hoses at firewall to and from heater core get hot.

What makes this problem better or worse?

Nothing

How long has your 2006 Ford Taurus had this problem?

The entire year of 2020 that we have owned the car