2004 Ford F350

Doesn't look like a common prob, (no replies).
T-stat prob. Would show low on your temp guage. Feel around under hood when blows cool - is engine hot?, Are heater hoses hot? (In AND out of core?) If they are the prob is likely a"blend door" or something letting cold air in WITH the recirculating. A PENCIL falls down the defrost and can do strange things to doors.
How about a valve on engine side or a hose kinked - check on top of right (passenger) valve cover - is there a valve there and the vacuum line controlling it fell off?
When you're feeling around you should be able to tell where the heat is and where it's not -your problem is at this transition. If the heater core's plugged it will do this symptom but I've not seen that in a while.