We replaced the thermastate on the Chevy Cavalier. It is still running hot and heater will not kick in.

So did you check the gauge and the sending unit ?
Either component could be faulty.

Have you checked the electric fan. It is possible that the fan sensor is malfuncioning causing the fan to not turn on. Also, the coolant needs to be mixed with water at the proper rate to cool properly. You can check the fan fuse or relay. If the heater is not puting out hot air, the heater core could be clogged, not allowing the coolant to circulate.

it could be air but it could also be a faulty radiator cap

is the cooling fan kicking on?

Your heater core has a small leak. You can try to fix it with some rad sealant, the kind you put in your radiator, like "Barsleaks" or something. I find the aluminum filing type work the best. When your rad is low, mix the filings in a few cups of water, and then add to the radiator, and let it run for a while. If the leak is more than a pinhole, it probably won't last long, and the heater core will need to be replaced.

it seem that the root of your problem maybe caused by by radiator the heat exchange maybe restricted by dirty fins or corroded passages with in the radiator. This is proven when your temp goes down when your a/c is on. the airflow increases when the a/c fan is on. also make sure your fan turns on high when engine is hot. The heater core problem maybe caused by the removal of thermostat. the thermostat control the flow of cooling water and by removing it it forces more pressure to the heater core thus causing it to fail prematurely. you really need to fix the high temp problem, removing the thermostat will just contribute to more problem not to mention a slow warm up of the the engine (delayed heater reaction) and may contribute to high emmision discharge. The radiator usually cost around $150.00 + 1 hour of labor a lot cheaper than $300 - $500 bill to replace the heater core.

Feel the radiator is it getting hot? If it's cold it may be stopped up.

Yes it does have a electric fan, mine went out on my 2003 and I just changed the electric motor itself. Autozone offered the entire fan with motor or they offered just the motor. I chose to replace the motor only because I knew the fan blades and housing was fine. I had to drop the fan down and take out the entire assembly from the bottom but overall the process was a 3 out of 10 on the difficulty.

there is a relay for the fan....trace the wires from the fan to the relay....should be on the radiator support or the housing for the rad.

have you replaced the coolant tempeture sensor.