u asked if old parts could be the problem, probably since u put in an old thermostat. so start there with a new thermostat. does sound like a bad thermostat, bad water pump or slowly leaking radiator. could be a leak in a hose. blown headgasket u would have trouble driving it. the car would not want to run or move. the symptoms of slim in the oil cap, white smoke come later. u would notice too alot of coolant is gone. water pumps make a bearing noise also.