Q: car won't start after it has been runninf and then cut off on 1991 Toyota Corolla

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The car will start right away when it has not been running. After it has been running and then the engine cut off the car will not start. The battery, starter, and the alternator are in good condition. Why won't the car start after it has been running for a while?
(1) Answer
(2) Comments
I have this same problem on my Saturn. It starts right away in the morning and right away after work. But if I run an errand, the car will start - I get to my destination - I get back in after my quick run - and the car does not turn over. I wait 30 or more minutes before it turns over....just like nothing was wrong with it in the first place. Like a cooling period. Battery is good, cables good, car runs smooth when it is turned over and running....I'm at a loss....I've a Saturn SC2 1997. 4 cylinder.

Can someone answer why this is?