Any ideas about why my car is overheating?

Okay so… 2000 Jeep Cherokee, newly rebuild engine, new radiator, check engine light is on…

Everything will start normally. I’ll drive, looking at the temp gauge, the temp will gradually rise. It will not stop at 210 F like normal. It goes right passed that to about 250 F, the check gauges light goes on. It will stay this way for a few minutes then it cool down and go back to the normal 210 F. It usually stays normal for the rest of the ride. There isn’t any steam coming out when it overheats. I’m thinking this just might be a thermostat problem or something like that. Does anyone have an ideas?