Overheating

It overheats it does not smoke out the tailpipe and there is no water in the oil. I changed the thermostats with a cheap one from advanced auto. It blows cold air even though it is full on fluid. The fans would kick on every once in a while but not all the time when it would overheat. So I took the thermostat out and ran it the car gets to normal operating temp and stays there but still throws cold air and the fans turn on and off as the car starts to get hot and seem to work as they should and I fit gets a little hot like three quarters the way and I rev the gas the temperature falls back down to normal operating range. A mechanic friend said he believes it is a head gasket but besides overheating there does not seem to b any other symptoms. Could it be I am not using a OEM thermostat is it that much difference or could the water pump is weak? I do not know what else could it be. Thanks for any help.