Ok i just purchased a 04 f-250 with 6.0 diesel. I got the truck in florida an I live in NC first 450 miles everything went great then it started to over heat

Only thing I know that I did different is i was going to try to check the coolant level at about 300 miles when I got fuel but when I went to ta ethe cap off it was to warm so I tightend the cap back could it be the resovior cap ? I got the truck cooled down some and put close to 2 gallons of water in it. Afer that it runs cool when I go into SC the outside temp was low 50's and the engine temp went to the very bottom of normal range just above cold every once in a while it would warm up a little but stayed cold most the way home. I know next to nothing about diesels except equipment.
Could the water have just been low ?
Could the thermostat have stuck closed then stuck open ?
Also when I tried turning the heat on even when the engine was almost normal the air comes out cold ?