Running straight water is not the reason for overheating, everything I own that has only been driven in the summer ran on pure distilled water, boiling point is determined by the pressure of the cap, a junk cap will over heat a car faster than anything. Fill the car with water let it run till the upper hose is warm with the heater on and the cap off, that should purge all the air out if the system, top it off put on a NEW 16lb cap and you should be fine, as long as nothing is wrong with the motor internally.
