Installed new crate GM replacement 350 engine. It will run hot after initial warm up but after turning off and setting a few mintues it will return to normal temp and stay there city or open road until allowed to cool completely down. Then it will repeat overheating. Replaced themostat 3 times, Rad cap, sending unit, water pump and hoses. Also flush system (at home). Had simular problem before engine replacement but not the same.
Check the thermostat to see if it has a bleed hole and a little dangly thing in it. That is to allow the hot coolant over there to flow over to the thermostat and cause it to open. Without that bleed hole the heat can't get to the thermostat. It will migrate over there when the hot engine is sitting for a few minutes.
I had a similar problem on my '88 Grand Caravan. It was fine with the replacement thermostat for over five years, then gradually began climbing to "hot" after five miles, then would suddenly go to "cold", then up and down a few times before holding steady at "normal". Can only guess it started doing this after five years because it was sealing better. Had a student take it out and drill a 1/16" hole in it which solved the problem. I'll be driving it in about a half hour and it will work fine.
By the time the heat got to the thermostat over here, the gauge's temperature sensor over there was already getting too hot. When the thermostat opened, the cold coolant from the radiator rushed in and sent the gauge back down to "cold" and the thermostat closed again. Each time it took less time for the thermostat to open until it stayed steady.
If you want to prove this without drilling that bleed hole, prop the valve in the thermostat open by sticking in a small piece of a toothpick. Start with a cold engine and you'll see it doesn't overheat that time. The toothpick will wash out so the problem will come back the next time you start with a cold engine.