Agree to start with thermostat first. I had the water pump blow on me on my last vacation trip, in South Carolina while I was heading back to Maryland. I kept water in the car, but it never even came close to overheating. That was my original worry and I finally got to the point where I just stopped to put water in it, but the temp was fine the whole trip. I used a lot of water, though!
But when I got the car from my Father-in-Law, he indicated that the car had been running a bit warm for some time. I thought, sheesh, I'm just going to put a new thermostat in without doing any testing just because I don't know how long it's been in there. It has run cool ever since.
1987 300SDL 265,000 mi.
1982 300SD 325,000 mi. (and holding)
1956 Packard Clipper 150,000 mi.