My Previa won't start after I've been driving it for awhile and it's hot and I'm trying to start it after a 10 to 15 minute delay. However, an hour or more later after it's cooled off, it will start. Do you have any idea what is causing this dilemma?

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It only started to do this recently. I changed the starter a few years ago when it did it once then but in the last 2 weeks it's done it 3 or 4 times. Once again, if I try to start it 10 to 15 minutes or so after I turn it off and after a long drive it won't start. But if I wait an hour or more, it will start. An authorized Toyota service dept. can't seem to figure out what's wrong with it.