What else could make my Neon engine heat up?

Well the water pump could be leaking or the radiator or the head gasket or the heater core the fan might not be working . Lots of things . First thing is figure out where all the coolant is going and then fix that and hope you didn't hurt the engine .

If you had to do this 5 times,you have a BIG problem.I would strongly urge you to either stop driving it,or start looking for the problem.

As far as what is causing it:

Leaking radiator/Leaking water pump/stuck thermostat/non functioning cooling fans/blown hoses/and or bad head gasket/cylinder head which was probably caused by you continuing to drive it with this problem

None of the guesses are near correct.

Radiators cause overheating. No other part can be replaced to solve your problem.

Go to a RADIATOR SHOP,not an auto repair, and get an opinion.

Nothing will help your problem so stop wasting time ,money and effort and get going.

You could have a bad or loose fan belt! Or the Water Pump is going out!

The most common problem involves the electric radiator fans or the relays/sensors that operate them. My guess is that your fan(s) aren't working.