The light should not come back on as long as you plugged it back in. Thats what that light means, the sensor may be going bad then, but that is your low coolant level light.

The only other option is possibly your alternating going out. Low battery voltage can cause crazy things. Take the car to auto zone, advanced, whatever and have them test the charging system. They will do it free on the spot, and then you will know for sure if you are looking at a new alternator or not.