I'm not a 560 owner, but have gone thru similar situations with another 126 car.
Coolant raises the boiling pint and lubrictates various cooling sys. components. By running straight water, you are lowering the boiling point and providing no lubrication for your system.
It's possible that you have an excessively high concentration of coolant. Too much coolant can cause overheating. Should be no more than 50/50. It's also possible you have air in the system. Perhaps someone will chime in with 560 air-bleed procedures.
How about your thermostat. Is it installed correctly. There's an air-bleed valve on most that needs to be at the highest position.