Overheating

Bad water pump, defective thermostat, radiator cap, fan motor, fan motor sensor, radiator may need to be flushed, old fluid may need to be changed...blogged vent line....

And don't forget possible head gasket.

It runs just fine, the gauge shot all way up and temperature light came on. Then gauge dropped immediately to cold. 30 minutes later shot back to high and check engine light came on. Still no sputtering no noises, running smoothly, but gauge stuck on cold and check engine light stayed on. Wouldn't head gasket make engine run rough or sputter? At least that's what my experience was a long time ago

Then make sure the coolant level is full, make sure air is purged from the cooling system by leaving the radiator cap off until warm up, coolant may spew over, but that would be the air working its way out, keep filling as necessary until full. No white smoke out the exhaust? Engine oil checking more full or look milky?

We ran a check on it and it said the engine coolant temperature sensor malfunctioned. I bought the part and hope it takes care of it.

That will do it. False readings from temperature sensor, you are fixing more than you know with that. All the other sensors are adjusted by the information the temp. sensor sends to the pcm.