2005 Hyundai XG350L-Why does vehicle need to sit between re-starts

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Recently, (about a month now), my vehicle has to sit for a while before it will restart. Has a new battery, and no problem with alternator., and runs fine otherwise. The failure pattern is exacting: - Starts fine in the morning, but if I have to stop, (and turn car off), it will fail to start, unless it has set for approximately an half hour. At that point, it cranks right up with no problem.