just my 2 cents worth, if you are getting air in your cooling system and losing coolant with no visible signs of loss, dripping on the ground etc, the most likely case would be the head gasket, ( this doen't mean you should have milky oil) if the gasket is blown there are 2 sides to a head gasket you can get a leak from one of the water ports directly into a cylinder bore with out actually affecting the oil, if the motor has overheated it would most likely to be a warped or cracked head/blown gasket, which of course would allow coolant to get into a cylinder, and also the motor would run rough, maybe not all the time as at different temperatures and coolant pressure would be a factor.
I don't believe a blocked heater core would be the problem, the only problem with a blocked heater core would be your heater, as a heater core has a tap on it anyways when you turn your knob from red to blue on the heater control you are actually BLOCKING coolant from flowing through your heater core.