You suggested distilled water and run engine for 15 minutes.
Distilled water will not clean any area in the cooling system. It will do more harm then good, the engine coolant is a much better cleaner. Not even All engine coolants are good for a toyota (they have to be free of 2 particular chemicals normally used in antifreeze)
If the engine coolant expired simply drain and replace (there is a proper way to drain ALL the liquid from radiator and cylinder head, not by simply opening the drain pipe)
Others in this thread (not you) sugested distilled water in the cooling systen to clean the throttle body coolant sensor. One should never do that. If there is a faulty thermostat, replace it, if the throttle body is dirty, remove it and clean it (simple logic) But please, leave the cooling system alone, toyota invested milions in research and development for the coolant