Neanderthal, you shouldn't run straight water during the summer, or anytime. Compared with 50% mix coolant, straight water has a lower boiling point. Once you have steam instead of water at the water jacket surfaces, heat transfer suffers. Search the archives using "nucleant boiling", where I've posted more on this subject.

The original question was whether it's okay to flush with tap water. It has no detrimental effect on the system if, at the end of the flush, you displace as much of the tap water as possible with distilled water. This allows you to use copious amounts of water for an effective flush without having to worry about the cost of distilled water.