One easy way to distinguish between a head gasket and an air problem is to remove the radiator cap (not the cap on the plastic reservoir) when the motor is cool; and see whether the coolant level is up to the top of the filler neck. If it is not absolutely full; fill the radiator to the very top. It is essential to not use 100% coolant; as coolant is designed to be mixed with 30-60% water, in order to transfer heat properly out of the engine. Pure coolant will make the engine overheat.
There also should be an air bleed valve in the thermostat housing; which is intended.to be opened while filling the radiator, in order to permit the trapped air to bleed off. Using this bleeder valve will enable more air to be removed than just letting it come out through the radiator cap. The heater temperature control should also be set to "hot" when filling the radiator, and when running the motor the first time after the cooling system has been worked on. This will allow the air in the heater core to be released.
If the thermostat was installed upside down (with the spring on the side away from the motor) this would make the motor overheat. If the fan belt is not turning the water pump; that would also do it.
Check the above steps first. Once those factors have been eliminated; if there is a head gasket leak; it can easily be detected by filling the radiator and connecting a radiator pressure tester to the radiator filler neck. Then pump up the system to about 10 psi, and watch the gauge to see if the pressure holds. If the pressure does not leak down in 2 minutes; reduce the pressure to 5 psi and then start the motor. If the pressure leaks down when the motor is not being run; or rises above 10 psi in the first minute of operation; there is a head gasket leak. This can be confirmed with a chemical test of the radiator fluid.