My Chrysler Neon is heating up and is making continuous warning beeping sound(longer than the normal warning sound) what faults can I expect?

Have your codes read on the car see if any fault codes. You can take it to a local auto parts store such as autozone and they will read it for free. This will give you a good starting point to pinpoint your problem

Thanks for the advice joemom, but is it safe to drive the vehicle to an Auto part store?I'm scared to cause more damage.

Is it just getting hot or truly over heating, it also depends how far the auto store is, a few miles I would say its ok. If you can get there and any codes show, make sure try and let the car cool down and drive home. Before you do anything, Makes sure you have enough antifreeze in the radiator and the overflow tank is filled to the correct point as well. If any codes show post them here and we will try to help...