2000 Chevy Cavalier

If the engine is overheating, make sure the coolant is full. If it is, you may have to replace the thermostat. If that doesn't work, then my next suggestion would be to check the head gasket.

As far as the heater core, start the engine, let it warm up to normal operating temp with the heater on high, and feel both heater core hoses (supply and return). Both should be hot. If they are, the heater core isn't plugged. Please keep in mind, a bad head gasket can cause air pressure to get into the cooling system. Many times that will cause an air pocket that will prevent the heater from working and the engine to over heat.

I would start simple, the thermostat.

Let me know what you find or if you have other questions.

Joe