I had the same problem on my 06 about 2 years ago. I cant for the life of me remember the name of the bad part. I remember it had something to do with the heater (and this was in the summertime, my ac would only come out the defrost vents) though. Only cost about 90 to fix from Ford... Took them about an hour.
2006 Ford F-250 King Ranch w/ 6.0L Deisel 149,000 miles *Daily Driver/Hauler*
2006 Ford F-250 Extended Cab XL w/ 6.0L Diesel 55,600 miles, Work Truck
NEW ADDITION! 2010 Ford F-250 XL Long Bed 6.4 diesel. 2,100 miles, Farm Truck