Just throwing this out there. Hot start problems can be the result of a going bad fuel pump relay that's located in that square fuse box behind the battery. The symptoms are: starts cold but if you warm up the car in park it for 20 minutes like going into the store it won't crank unless you cycle the switch about a dozen times. Turned out it was the fuel pump relay partially broken inside. It's a common relay that Toyota uses and can be found on other vehicles.
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