I have a 2010 Ford Escape that was doing the same thing, ended up being the Air door actuator. There are two, one that controls hot/cold, and one that controls where the air flows. The one that was broken for me was the one that controls where the air flows, which was located on the drivers side next to the break pedal. Here's the part I needed:
https://shop.advanceautoparts.com/p/dorman-oe-solutions-air-door-actuator-mode-604-224/10188638-P?searchTerm=blend+door+actuator