This 2006 F350 6.0 had this problem last summer but the towing is infrequent enough to not get the test for the fix. The problem occurs when towing on 90F or higher days. The a/c doesn't quit but the vent temps go up and it approaches uncomfortable. It gets even warmer on hills. The system cools GREAT when I checked it. As good as any -> 2007 SD I have ever worked on. I changed pressure cycling switch as a guess since I could not duplicate the issue thinking the switch got hot and cycled too much. I already had the owner checking for freezing and it did not freeze as the cooling would return as he pulled over to look at stuff. Frozen evaporators take several minutes to thaw if it is bad enough to raise temps. The fix (so far it's working) is to seal the evaporator lines going into the case. The foam seals are disintegrating with age and I see it on many. When towing the engine fan may run near 100% at times but it runs at lower percent most of the time on 90+ days towing 17K pounds like this truck even on flat ground. It seems the hot air blowing in engine bay is blowing into the evaporator case and raising vent temps. I had already blocked heater hose for one of his trips last summer in case the ATC was not keeping hot water valve closed and that did not fix it. I had him raise temp on ATC when it occurred until the recirc would go off and he could hear blower noise go up and then back down when the temp was lowered again so that was eliminated. I have seen so many of these with those foam pieces gone that I disregarded it until now. I used a short piece of a/c line foam tube and pushed it into the case opening around the pipes. He called me yeaterday as he drove across west Texas loaded and said it stayed cold. I will use cork filled a/c line wrap later but I had none on hand the other day. I don't think tht black fom suction line covering will last in engine bay but the butyl/cork stuff will.