An issue that is not fixed after repeated attempts is covered under lemon laws in your jurisdiction. Contact Honda Corporate directly. Tell them your concern, and that if the heating issue is not resolved to your satisfaction, you will be returning the vehicle to the dealership for a full refund. That should get their attention in a hurry.

 

Two Fits, 130,000 miles total - no issues with the heating system - although I'd like it to put out more heat!

 

The heater mix control is a mechanical device. The turning motion pushes or pulls a cable. The ends of the cable are attached to the dial or an adjustment arm (or whatever is used in the fit). The cable sheath does need to be attached firmly so that the cable can slide inside of it.

When I disconnect it on my Integra, the instructions were to simply adjust the dial fully one way, adjust the other end to where it's supposed to be, then secure the cable sheath to so that it retains that position.

Most of the problems that I've seen is when the cable sheath attachment comes loose.

I've never worked on this on my Fit, but by removing the glove box, I can see the contraption and might be able to work on this from there.

 

This video may help.

https://youtu.be/5r_1d7xo388

 

Ah, that's your video! I was going to say that it's an unusually good YouTube DIY video. In so many of these, the camera is moving all around, out of focus, and the speaker is mumbling. Nice work!

That pinch clamp seems iffy. I'd prefer something more positive, like a screw or a bolt. It looks like you would pull that cable out, reposition it, and snap it back in. Is that locking piece plastic? Before I did any adjusting, I'd check the actual position of the thing that is moving to control the temperature. Maybe it's opening/closing far enough, but it's just not registering right on the control knob. I had that situation with a car a few years ago. I got hot and cold air, but the dash control was off by a bit. I left it alone.