My run to the dishwasher is not particularly long but it still takes a good half gallon before it starts to get warm water to the tap or to the dishwasher. I used to run the hot water until it got hot and then power up the dishwasher but I stopped doing that and let the dishwasher heat the water. My dishwasher is a mid 2000's energy star model and I've clocked it using 6 gallons of water during the whole wash cycle. It doesn't heat the 10 minute "pre-wash" cycle or the rinse cycle but the main wash cycle, the one that lasts for over an hour(maybe even almost 2) heats the water.
If I use the light cycle on my dishwasher it won't heat the water at all. I preferred this setting in the summer but in prior years my winter house temperature is far too cold to heat up the dishes and the air in the dishwasher using that cycle, I literally put my hand in there and the water was barely over lukewarm.
I don't heat my hot water tank hotter than I need to for a comfortable shower and getting sick is far more expensive than heating a single digit number of gallons of water to a slightly higher temperature so I let the dishwasher do the job with whatever its internal thermostat is set to. It uses less than 2kwh including the water heating and the pumping with a normal wash cycle with water heating on and heated dry. If the difference is a single kwh, I think its worth it.
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