If you get this figured out, please reply to this thread. I've had that problem for the past 2 or 3 years now. Replaced the water valve - no change. The only way I get cold air is if I don't use the Auto function, but I select the Top and Middle air buttons. The face and top vents will blow cold, but when the car gets hot, the vents by my feet blow hot as hell.
Next step is to remove the dash, however I don't have the time to take the dash out, try and figure out what the broken part is, order the part, wait for it to be delivered, and then put it all back together. I suspect its an actuator motor or a stuck vent... however I can't find individual parts for that on realoem.com. If I even had a guess at the parts it could be, I'd start buying them and replace them when the dash is out. Realoem shows the center vents as one unit. If someone who has done this knows of the individual part numbers that I can order, PLEASE pass that on as I'm so sick of this issue.