Why won't my 92' Previa start sometimes?

I've had my 92' Previa since 93'.  Recently, it has developed a starting issue.  It seems to happen after I've been driving it for several hours and when I stop to get gas or some other brief errand, it won't start again after 10 or 15 minutes.  If I wait an hour or more then it will start.  A Toyota master tech. says it's not the starter or alternator.  He changed the belts but the problem persisted.  Then he remembered another vehicle with the same issue that he solved by changing the battery so we did that but the problem persists.  He is currently trying to present the problem by running the van for several hours, turning it off and then trying to start it after a 10 to 15 minute interval.  So far he has been unable to get it to present the problem so to them it looks like nothing is wrong with it.  Every time before today when they've had it at the dealership's service dept., it has started every time because it has sat there off for quite awhile before starting.  It's seems like some part is cooling off in the interval and then it will start but if you try to start it shortly after turning it off and after driving it for several hours, it won't start.  Do you have any idea what's causing this problem?