I've not so long ago taken my dash to bits to get to grips with this very problem. In my case it was the drivers side that stuck.
You can get to the motors by removing the glovebox, and the bits surrounding the radio area. I had to deal with the drivers side, so this may be alittle different. One, or two motors control air direction and are mounted together on a sliver coloured plate, the one that controls temperature is mounted sperately. The motors can alll be removed by undoing the correct screws.
Take all the covers off, then play with the AC controls. You should see clearly a change in the position of the motor for temperature control as it is attached to a load of white plastic arms and stuff. Turn the temp up and the motor moves one way in lumpy little jerks, and down goes the other way.
On my car it turned out that the issue with temperature control wasn't an issue with the motor or the control arms, but the electronic controls. The flaps moved, the motors worked, just the electronics randomly set full hot, when I had requested full cold and AC. After taking it all to bits and checking it all, I decided to live with it. I got a much better performance when I regassed the AC. This kind of fixed the issue as I didn;t get extreme hot air, just tepid blown in my face!