Before changing the oil, run a quart of kerosene on the oil and run around town for a bit. Or add a quart of ATF and run around for a few days. That may clean things up right away,..
Check all the coolant hoses, and take the time to install a new thermostat, cap.
I would say for such a road trip, cooling issues may be most probable problem
Ask to see if the seller knows when the timing belts were serviced last