Temperature malfunction

At random my car will start running hot (it usually stays a little below or right at 200 degrees) when it gets a line over 200 degrees it usually will then continue heating up and overheat. Then I pull over let my car cool down and restart it and it will be fine. Sometimes it blows the coolant out of the overfill tube and sometimes not. Low coolant light goes on and off. Replaced thermostat, radiator cap and water pump.
Also, a while back just the knob that controls temperature inside my car broke off and I could still control the temperature with the dial shaft that the knob broke off of. The dial shaft was loose in there so I would wiggle it and then when I would push it a little up and towards the passenger side it would blow hot air. But now the dial shaft broke off too from wiggling it so it is just flat where the knob is supposed to go. It broke off on the cool temperature and now I can't figure out how to reconnect the dial shaft to be able to heat up my car. Is there anyway I can bypass the temperature control dial to heat up my car still with out replacing the whole HVAC system? Basically can I jerry rig the shaft to work again? Can I run some wires in some of the connect holes on the panel?