My 01 cavalier starts then shuts off?

If your car started to over heat, and now is shutting off, it could be a sensor not alowing it to idle to prevent damage to the engine. Check your coolant, and if it's low or even empty get some coolant from an auto part store and if it's not low or empty, make sure that when it's started coolant is flowing to the motor. If that isn't your problem, check your engine sensors. Cavaliers are touchy cars and tend to have questionable problems like this. Hope I helped.

is any of your dashlights on, like check engine, low coolant, or security? most auto parts stores will loan engine diagnostic tools that simply plug into your car under the dash and will tell you if any sensors are bad. ive never seen a car that will start and dye simply from overheating, especially if the engine is cold, but if it was puttering it could be any number of simple things causing it to not run like fuel pressure regulator or throttle position sensor which the engine diagnostic tool should figure out. if the engine diagnostic tool finds something wrong it will give you a code like p0121. then you can either ask what to do at the parts store or look up the code online and go from there, good luck.