i'm pleased you havent lost any coolant, thats a very good sign. looks like you've been lucky and noticed the engine overheating before the head gasket was affected, well done. did you manage to get any hot air out of the heaters yet? if you get heat coming out of the heater vents you can assume you dont have air stuck in the cooling system and dont need to bleed it. i dont see how you could have air if the coolant level has not dropped and there is no sign of a leak or head gasket failure. you must check for hot air coming out your air vents before you do anything else.
assuming you do get hot air coming out the vents, i would suspect a stuck thermostat is causing the engine to overheat, although the problem could just as easily be a blockage in the cooling system from a build up of corrosion and slime. if your radiator isnt getting hot it is usuallly due to a stuck thermostat. the thermostat contols the flow of coolant around the system, usually it will open when hot to allow the coolant in the radiator to flow around the whole system, cooling the engine. when its stuck shut the engine overheats while the radiator stays cold. coolant cannot pass through the stuck thermostat.
i would recommend you get the cooling system drained, flushed and refilled, and at the same time have the thermostat tested. you can do all this at home easily, with the help of a haynes manual i'm sure you wil find it an easy job. you can test the thermostat using a cup of boiling water. if it opens in the boiling water its fine. if you get this done at a garage it wont cost the earth, it is part of normal servicing and should be done every 2 years. many people ignore this, thats how problems are caused.